SUM Cosmology - User contributions [en]

Stationary Universe Model (SUM) - Deutsch

2026-02-21T13:23:56Z

Admin: Disclaimer

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

<div style="color:red">
-----
'''Diese deutsche Seite wird noch im Sinne der englischen Seite "https://peter-ostermann.de/wiki/index.php?title=Stationary_Universe_Model_(SUM)" vervollständigt und ergänzt'''
-----
</div>

Das Modell '''SUM''' ('''Stationary Universe Model''') wurde seit 2001 von dem Physiker ''Peter Ostermann'' aus der Voraussetzung eines
ewigen, unendlichen Universums als offenes Projekt (''work in progress'') entwickelt und auf Basis der
originalen [[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]]
[[wikipedia-de:Albert Einstein|Albert Einstein]]s <ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25.
November 1915, 844-847 – (reprint Doc. 25, CPAE Vol.
6)</ref><ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 –
(reprint Doc. 30 CPAE Vol. 6)</ref> ohne [[wikipedia-de:Kosmologische Konstante|Kosmologische Konstante]] als vernünftige Alternative<ref>P. Ostermann,
"''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054,
2002/04</ref> zum numerisch außerordentlich erfolgreichen
[[wikipedia-de:Urknall#Expansion des Universums|Urknallmodell]] phyikalisch
formuliert. Es wurde beim 12. [[wikipedia-de:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]<ref>P.
Ostermann,
"''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.),
Proc. MG12, W.Sci., 1408-1410, 2012;
[http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref><ref>P. Ostermann,
"''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background
Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.),
Proc. MG12, W.Sci., 1373-1375, 2012;
[http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref> in Paris vorgestellt (MG12 2009, zuvor
bei der DPG-Frühjahrstagung<ref>P. Ostermann,
"''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref> 2007
Heidelberg, erste pre-prints bei arXiv.org). Gegenüber dem aufgrund
exzellenter scheinbarer Bestätigungen seit langem vorherrschenden
[[wikipedia-de:Kosmologie|Standard-Modell]] (''Konkordanzmodell'') in Form der
[[wikipedia-de:Inflation (Kosmologie)|inflationären]]
[[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Kosmologie]] stellt SUM auf Basis eines
neuen Linienelements ein Konzept dar, das im Gegensatz zu der trotz
übereinstimmender Motivation überholten [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] mit
aktuellen kosmologischen Beobachtungstatsachen vereinbar scheint. Trotz
verblüffender Erfolge hat das Modell hinsichtlich diverser Details nicht innerhalb weniger Jahre den hochentwickelten Stand der nahezu
ausgereiften Konkordanzkosmologie erreichen können, sondern befindet
sich noch in einer Anfangsphase; es versteht sich als Ermutigung im
Sinne der ''Aufklärung'': "sapere aude!" (wage zu denken).

<div style="color:red">
Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allowing for the solution of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.
</div>

Das neue kosmologische Modell SUM eines stationären
Hintergrund-Universums beinhaltet keine [[wikipedia-de:Expansion des Universums|Expansion des Raums]]. Es geht aus von der physikalischen
Tatsache, dass aus Nichts nichts entsteht. Das [[wikipedia-de:Weltall|Weltall]] wird als eine insgesamt beständige Gegebenheit betrachtet und im Sinne des
''stationären'' – nicht aber statischen – ''Universums'' von unserem
''[[wikipedia-de:Urknall|evolutionären Kosmos]]'' unterschieden. Alter und Ausdehnung des Universum sind demzufolge unendlich, nicht aber unser Kosmos als
Teil davon.

Was sonst als 'Alter des Universums' bezeichnet wird, stellt sich aus
Sicht von SUM heraus als das Höchstalter makroskopischer Strukturen wie
dem von Sternen, Galaxien, (Super-)Cluster gegebenenfalls bis hin zu dem Höchstalter ganzer Kosmen. Scheinbar gegenteilige Beobachtungen
ältester Galaxien könnnen von einem einzigen gemeinsamen Ursprung nicht
überzeugen. Dies steht in Analogie zu der alltäglichen Erfahrung, dass
das Höchstalter individueller Menschen nicht etwa das Alter der gesamten Population beweist. Im Unterschied zur natürlichen Suche nach der
vitalen Vergangenheit unseres evolutionären Kosmos macht es keinen Sinnnnach einer historischen Entwicklung des ewigen Universums zu fragen.

Trotz gemeinsamer Voraussetzung des ''[[wikipedia-de:Kosmologisches Prinzip|perfekten kosmologischen Prinzips]]'' unterscheidet sich das Model SUM mit statistisch konstanten Werten der [[wikipedia-de:Rotverschiebung|Rotverschiebung]] kosmischer
Strahlungsquellen fundamental von der [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] eines
expandierenden Universums<ref>H. Bondi & T. Gold,
[http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref><ref>F. Hoyle,
[http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical
Society, vol. 108, 372-382, 1948</ref>. Die mathematisch exakt
abgeleiteten gleichbleibenden SUM-Rotverschiebungswerte entsprechen den
nach Voraussetzung statistisch gleichbleibenden [[wikipedia-de:Euklidische Geometrie|euklidischen]] Entfernungen in ''universalen Koordinaten'',
die aus historischen Gründen auch als ''[[wikipedia-de:Entfernungsmaß#Mitbewegte Entfernung|mitbewegt]]'' bezeichnet werden (''comoving coordinates'').
Nach einer zunächst rein mathematischen Ableitung der ''stationären''
[[wikipedia-de:Hintergrundstrahlung|Hintergrundstrahlung]] mit [[wikipedia-de:Plancksches Strahlungsgesetz|Planck-Spektrum]] (ohne Zurückführung auf einen
[[wikipedia-de:Urknall|Urknall]]) wurde eine SUM-Vorgängerversion<ref>P. Ostermann,
"''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''",
arXiv:astro-ph/0312655v6, 2013</ref> weiterentwickelt und zu
''Model of a Stationary Background Universe Behind Our Cosmos'' (2013)
ausgebaut. - Sämtliche zugrunde liegenden Arbeiten stehen auf
[http://independent-research.org "independent-research.org"] zum
Download bereit.

== Das stationäre Linienelement ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – Die
Zuordnungen (<math>\Omega_\mathrm{M}</math>, <math>
w_\mathrm{M} </math>,
<math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0,
0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') =
\mathrm{e}^{Ht'}</math> [obere graue durchgezogene Linie], eine
erste Alternative zu <math>a_\mathrm{CCM}(t')</math> mit
größerem Wert <math>\Omega_\mathrm{\Lambda}</math>) [blaue
gestrichelte Linie], das heutige Concordance Model
<math>a_\mathrm{CCM}(t')</math> [blaue durchgezogene Linie], das stationäre ultra-large scale Universum
<math>a_\mathrm{SUM}(t') = HT'</math> =
<math>1+Ht'</math> [rote gerade Linie], eine zweite Variante zu <math>a_\mathrm{CCM}(t')</math> mit kleinerem Wert
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken
line], das Einstein-de-Sitter Modell <math>a_\mathrm{EdS}(t') =
</math> <math>(1 +
\mathrm{3/2}Ht')^\mathrm{2/3}</math> [untere graue durchgezögene
Linie, favorisiert vor dem SNe-Ia Durchbruch]. Im Kontrast zu anderen
vergleichbaren Werten scheinen die CCM best-fit Parameter
<math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid
line) festgelegt durch die Bedingung, dass ihre Linie den
SUM-Skalenfaktor (rot) an seinen 'Grenzen', d.h. bei HT' = -1 und bei
Ht' ≈ 0 heute treffen sollte. ]]

Im Unterschied zu ''statisch'' besagt ''stationär'', dass ein Zustand
insgesamt gleich bleibt, obwohl sich einzelne Bestandteile ständig
verändern können. Dem Konzept SUM liegt, anders als bei der
''[[wikipedia-de:Induktion (Philosophie)|induktiven]]'' Entwicklung der
[[wikipedia-de:Urknall|Urknall-Kosmologie]], ein ''[[wikipedia-de:Deduktion|deduktiver]]'' Ansatz
zugrunde. Dabei genügen zwei [[wikipedia-de:Postulat|Postulate]], um das hier
zugrundeliegende stationäre [[wikipedia-de:Metrischer Tensor#Linienelement|Linienelement]] abzuleiten:

* Postulat I – In Bezug auf hinreichend große Skalen ist das Universum stationär, homogen und isotrop;
* Postulat II – Abgesehen von lokalen Abweichungen ist die universale Lichtgeschwindigkeit ''c''* = ''c'' .

Aus diesen beiden außerordentlich einfachen Postulaten ergibt sich das
SUM-Linienelement d''σ''*SUM eines räumlich
''flachen'', nicht leeren Universums eindeutig zu:
<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math> .
Hier steht ''H'' für eine wahre ''Hubble-Konstante'' (die im Unterschied zum zeitabhängigen ''konventionellen'' [[wikipedia-de:Hubble-Konstante#Definition|Hubble-Parameter]] ''H''0 der
[[wikipedia-de:Urknall|Urknall-Kosmologie]] als ''signifikant'' bezeichnet wird); die Abkürzung d''σ''*SRT steht für das Linienelement der [[wikipedia-de:Spezielle Relativitätstheorie|speziellen Relativitätstheorie]],
wobei das zusätzliche Symbol
'<math>\,</math>*<math>\,</math>' bei jedem
Auftreten auf die Besonderheit hinweist , dass sich die entsprechenden
Größen auf ''universale Koordinaten'' beziehen (neben den
'[[wikipedia-de:Entfernungsmaß#Mitbewegte Entfernung|mitbewegten Koordinaten]]'
''l''<math>\,</math>* auch die 'konforme Zeit'
''t''<math>\,</math>*). Gemäß SUM stimmen die universalen
Koordinaten immer wieder vorübergehend überein mit den ''[[wikipedia-de:Umgebung (Mathematik)|lokalen]]'' [[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlängen]] und
[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeiten]] der speziellen
Relativitätstheorie. Aus dem ausgeschriebenen Quadrat des Linienelements ist die Konstanz der universalen [[wikipedia-de:Lichtgeschwindigkeit|Lichtgeschwindigkeit]] mit c* ≡
d''l''<math>\,</math>*/d''t'' * = c (für
d''σ''*SUM = 0) sofort ersichtlich. Das
SUM-Linienelement hat weitere bemerkenswerte Eigenschaften.

== Rotverschiebung und signifikante Hubble-Konstante ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - Die SUM
Voraussage des im Rahmen der Lambda-CDM 'big-bang' Kosmologie völlig
unverständlichen Hubble-Kontrasts. -
Zwei verschieden Werte für die Hubble 'Kostante'
<math>H_{\mathrm{local}}</math> =
<math>H_{\mathrm{CCM}}</math> und
<math>H_{\mathrm{universal}}</math> =
<math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:'''''
Die blaue durchgezogene Linie repräsentiert die realen Werte
<math>z_{\mathrm{observed}}</math> der SNe-Ia-Messungen, die rote unterbrochene SUM Linie vernachlässigt mögliche 'peculiar flows' oder lokale Inhomogenitäten. Die maximale Abweichung <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c innerhalb
<math>z</math> < 0.027 entspricht einem maximalen
Kontrast <math>H_{\mathrm{local}}</math> /
<math>H_{\mathrm{universal}}</math> - 1} von ungefähr 9% an
diesem Punkt wo <math>H_{\mathrm{universal}}</math> ≈ 67
km/s/Mpc.

'''''-- Bottom panel (b)}:'''''
Innerhalb <math>r^* < 110</math> Mpc entspricht die blaus Linie <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc,
wohingegen der mittlere Wert in der Übergangszone (bis
<math>z</math> ≈ 0.13) ungefähr
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc beträgt. Die
Differenz führt von
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈
4.7% bis zu
<math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% und entspricht annähernd gerade dem Bereich des lokalen
Hubble-Kontrasts von 6.5% ± 1.8%., wie er von Jha, Riess & Kirshner
berichtet wird}.
]]

Es ist einfach falsch zu behaupten, dass die kosmische Rotverschiebung
eine Expansion des Universums beweist.
Die ''universale Rotverschiebung'' des Lichts entfernter
[[wikipedia-de:Galaxie|Galaxien]] und anderer Strukturen wird im Rahmen von SUM nicht als [[wikipedia-de:Doppler-Effekt|Doppler-Effekt]], sondern im Sinne einer erweiterten
Einsteinschen [[wikipedia-de:Rotverschiebung#Gravitative Rot- und Blauverschiebung|Gravitationsrotverschiebung]] verstanden, woraus sich
wie auch beim Experiment von [[wikipedia-de:Pound-Rebka-Experiment|Pound und Rebka]]
keine Fluchtbewegung zwischen Quelle und Empfänger ergibt (bereits
[[wikipedia-de:Edwin Hubble|Edwin Hubble]]<ref>E.P. Hubble,
[http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N.
Acad. Sci. 15, 168-173, 1929</ref> hatte eine solche Möglichkeit
in Betracht gezogen). Der Unterschied zur gewöhnlichen
[[wikipedia-de:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitativen Rot- und Blauverschiebung]] liegt hier darin, dass es sich im Falle von
SUM um ein ''zeitabhängiges'' Potential handelt, das sich aufgrund des
Vorzeichens immer als ''Rotverschiebung'' auswirkt. Aus der allgemeinen
Definition des [[wikipedia-de:Rotverschiebung|Rotverschiebungsparameters]]
''z'' =
''λ''<math>\,</math>beobachtet /
''λ''<math>\,</math>ausgestrahlt – 1
ergeben sich bei SUM mit
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
solche Werte, die mit der ''signifikanten'' Hubble-Konstante ''H''
unabhängig sind von der Zeit. Diese Werte gelten für Galaxien und alle
kosmologischen Strukturen, die sich in Bezug auf universale Koordinaten
(''x''*, ''y''*, ''z''*) nach Voraussetzung statistisch in Ruhe befinden (die Unabhängigkeit von der Zeit gilt auch für alle anderen Größen, die sich als Funktion der Rotverschiebung ''z'' schreiben lassen).
Insbesondere bedeutet deren Zeitunabhängigkeit, dass zusätzlich zu den
lokalen [[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlängen]] der SRT
nun auch den universalen Entfernungen
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
wegen gleichbleibender Rotverschiebungen entsprechender Objekte eine
reale, physikalisch messbare Bedeutung zukommt. Im Gegensatz zur
[[wikipedia-de:Urknall|Urknall-Theorie]] stellt die universale Entfernung ''l''* im
Rahmen von SUM also eine selbständige – obwohl indirekte – Messgröße
dar.

== Universale Zeit ''t''<math>\,</math>* und die Grenzen von Eigenlänge und Eigenzeit ==
Wegen der exponentiellen Form des Zeitskalars e''Ht'' * hängen relative zeitliche Änderungen e''Ht'' */ e''Ht''o* =
e''H''(''t'' *– ''t''o*) allein ab von
''Differenzen'' Δ<math>\,</math>''t'' * = ''t'' * – ''t''0*. Der gleiche Sachverhalt erlaubt es auch, für beliebige zusammenhängende Ereignisse (dies betrifft insbesondere auch [[wikipedia-de:Spontane Emission|Emission]] und spätere [[wikipedia-de:Absorption (Physik)|Absorption]] von Photonen) den universalen zeitlichen
Anfangspunkt jeweils ''t''0* = 0 zu setzen. Im
Unterschied zur jeweiligen lokalen ''Quasi-Eigenzeit'' ''t'' ' = ''T'' ' – ''T''H (mit der [[wikipedia-de:Hubble-Zeit|Hubble-Zeit]] ''T''H = 1/''H'') ist kein spezieller Punkt der universalen Zeitskala ''t''<math>\,</math>* ausgezeichnet.
Die universale Zeit hat weder Anfang noch Ende. Gemäß dem Linienelement
der in begrenzten Bereichen überall und immer wieder lokal gültig
bleibenden speziellen Relativitätstheorie
(d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) sind
die Intervalle von ''[[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlänge]]'' und
''[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeit]]'' stets miteinander gemeinsam
definiert. Wie daraus mathematisch folgt, können die sich in Bezug auf
das SUM-Linienelement ergebenden Näherungen
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
nur innerhalb lokal begrenzter Bereiche
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
des unendlichen euklidischen Raums (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2) jeweils
vorübergehend Gültigkeit beanspruchen (''R''H =
''c''/''H'' ist der [[wikipedia-de:Beobachtbares Universum#Hubble-Radius|Hubble-Radius]]). Gleiches gilt für alle
SRT-Konzepte überhaupt. Bei uneingeschränkter Gleichheit in den obigen
Näherungen aber würde das SUM-Linienelement in dasjenige der SRT übergehen, und der resultierende Einstein-Tensor würde unzulässigerweise verschwinden (was einer universalen Energiedichte Null und damit einem
leeren Universum entspräche). Diese Zusammenhänge ergeben sich aus einer zweifachen [[wikipedia-de:Koordinatentransformation|Koordinatentransformation]] ''t'' * =
ln<math>\,</math>(''HT''
')<math>\,</math>/<math>\,</math>''H'' und ''l'' * = ''l''
'<math>\,</math>/<math>\,</math>(''HT'' '),
wobei ''T'' ' näherungsweise einer ''Eigenzeit'' entspricht, die nach
obiger Ungleichung jeweils örtlich eingeschränkt ist.

== Die FLRW-Form des SUM-Linienelements ==
Wird nur die universale Zeit ''t'' * gemäß der ersten der beiden oben
angegebenen Formeln transformiert, so folgt das stationäre Linienelement in einer
[[wikipedia-de:Friedmann-Lemaître-Robertson-Walker-Metrik|Friedmann-Lemaître-Robertson-Walker-Form (FLRW-Form)]], und zwar mit dem einfachsten aller in Frage kommenden
[[wikipedia-de:Skalenfaktor|Skalenfaktor]]en
''a''<math>\,</math>SUM = ''HT'' ' zu

:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math> ,
ohne dass sich damit an den physikalischen Tatsachen etwas ändert. Es
lässt sich z.B. leicht verifizieren, dass der zeitunabhängige
SUM-Zusammenhang zwischen der Rotverschiebung ''z'' und der universalen
Entfernung ''l''<math>\,</math>* auch gemäß dieser FLRW-Form bestehen bleibt. Es ist im Hinblick auf die gesamte SUM-Kosmologie von
entscheidender Bedeutung, dass sich die auftretende
'Anfangs'-Singularität der örtlich eingeschränkten ''Quasi-Eigenzeit T'' ' = 0 nur auf lokale Bereiche bezieht und keineswegs ein Alter des
gesamten Universums darstellt. Stattdessen bedeutet sie, wie oben
gezeigt, eine jeweils auf ''l''<math>\,</math>* <
''R''H eingeschränkte maximale Lebensdauer
räumlich begrenzter evolutionärer Strukturen (in Bezug auf die
universale Zeitkoordinate entspricht ''T'' ' = 0 dabei ''t'' * = –oo.

== Energiedichte und negativer Gravitationsdruck ==
Die bei SUM offenbar der ''universalen Energiedichte'' entsprechende
Komponente ''G''00 des [[wikipedia-de:Tensor#Ko- und Kontravarianz|''kovarianten'']]
[[wikipedia-de:Friedmann-Gleichung#Herleitung|Einstein-Tensor]]s ist zeitlich
konstant. Demgegenüber scheint die [[wikipedia-de:Krummlinige Koordinaten#Tensoren zweiter Stufe|gemischt ko- kontravariante]] Komponente
''G''00, die bei Anwendung der [[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] auf lokale [[wikipedia-de:Ideale Flüssigkeit|perfekte Flüssigkeiten]] der
[[wikipedia-de:Phänomenologie|''phänomenologisch'']]''en'' Energiedichte entspräche,
abhängig von der ''universalen Zeit t''<math>\,</math>*.
Dass aber eine solche Abhängigkeit über beliebig große universale
Zeiträume im Unterschied zu lokal begrenzten
[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeiten]] ''t'' unrealistisch wäre, folgt wieder aus der Tatsache, dass kein spezieller Anfangspunkt der
Zeitskala ''t''<math>\,</math>* existiert.

Aus dem SUM-Linienelement ergibt sich zu jedem willkürlich wählbaren
universalen zeitlichen Anfangspunkt ''t''0* = 0
ein negativer Gravitationsdruck von –1/3 der ''[[wikipedia-de:kritische Dichte|kritischen Dichte]]'', dessen Existenz hier sofort einleuchtet.
Im Unterschied zu gewöhnlichen Teilchen in einem Kasten (die sich ohne
dessen Wände aufgrund ihres positiven Drucks sofort
[[wikipedia-de:Diffusion|zerstreuen]]) würden Galaxien innerhalb eines begrenzten
Bereichs des stationären Universums ohne negativen Gravitationsdruck (verursacht vom Gravitationspotential der Materie und Energie außerhalb) zusammenklumpen, was in Bezug auf hinreichend große Skalen nach
Voraussetzung nicht geschehen kann.

== SUM Vorhersage zweier verschiedener Werte für die lokale und die universelle Hubble-Konstante ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Links (a)-(e)''''': Der Vergleich der SUM magnitude-redshift Voraussage (für ''κ'' = 0) mit den original SNe-Ia Daten und der CCM-Voraussage zeigt eine unmittelbare SUM-Übereinstimmung auf universalen Skalen z > 0.1, auf denen das Universum am ehesten zu Recht als homogen und isotrop betrachtet werden darf. Die rote SUM-Linie fällt beinahe vollständig mit der blauen CCM-Linie zusammen (trotz - oder: wegen - der gegenüber der lokalen um 9% höheren ''universalen'' Hubble-Konstante).
 -- '''''Intermediate panels (b),(d)''''': Mit
dem in Abb. W2 gezeigten lokalen Hubble-Kontrast existiert nun eine
volle SUM-Übereinstimmung nicht nuur mit den SNe-Ia Daten des 'High-z
Supernova Search Teams' (Riess et al.) sondern auch mit Kowalskis 2008
Union 'world' Zusammenstellung des 'Supernova Cosmology Projects'
(Perlmutter et al.).
Offensichtlich genügen die Korrekturen von maximal <math>\mathrm
\delta z </math> ≈ 0.002 im Bereich <math>z {\mathrm{observed}}</math> < 0.027 für eine befriedigende
Übereinstimmung von SUM mit den Daten
im Falle des lokalen Hubble-Kontrasts
analog W2 auch im Bereich jeweils kleiner Rotverschiebungswerte.
 -- '''''Lower panels (c),(e)''''': In diesen CCM-Abbildungen sind die
blau-gestrichelten geraden Linien nach der Methode der kleinsten
quadratischen Abweichungen bestimmt und sollten sich im Idealfall als
kongruent zur jeweiligen z-Achse erweisen.
: ]]

In beiden Teilen der Abbilddung W2 repräsentieren die blauen
duchgezogenen Linien die realen SNe-Ia Messungen, wohingegen die
gebrochenen roten Linien (jeweils darunter) für SUM stehen. Eine
maxiimale Abweichhung <math> \mathrm \delta z </math> ≈
0.002 entspricht einem maximalen Huble-Kontrast von ≈+9%. Mit
<math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc würde das
<math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc innerhalb
<math> \mathrm{r^{\ast}}</math> < 110 Mpc
<math>(\mathrm \delta z </math> < 0.027) bedeuten,
während sich der Mittelwert in der Übergangszone gerade auf ungefähr
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc beläuft.

Nun wurde kürzlich von Riess als zweitem der zitierten Autoren ein
"lokaler Wert" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc
berichtet<ref>A.G. Riess et al.,
[http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ
826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]],
[http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
mit einer Toleranz von nur 2.4% (sowie 71.9 km/s/Mpc ±3.8%, was
annähernd übereinstimmt mit 72.8 km/s/Mpc ±3.3% in Bonvin e al.
<ref>V. Bonvin et al.,
[http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790
"arXiv:1607.01790]" </ref>.
Nahe bei Freedman's Wert von 72 km/s/Mpc
<ref>W. L. Freedman et al.,
[http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
aber in klarem Kontrast zu den von der
Lambda-CDM Kosmologie gemäß der neuen Planck 'high-redshift'-Messungen
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
vorausgesagten 67 km/s/Mpc – oder auch anähernd zu den 68 km/s/Mpc von
Cheng Cheng \& Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801
</ref>
bedeutet das ausgerechnet wieder einen Hubble-Kontrast von etwa +9%,
welcher Wert beinahe perfekt mit der original SUM-Vorhersage von 2007
übereinstimmt.

Anscheinend setzen die Autoren Riess et al. des neuen Reports zu Unrecht den gekümmmten Verlauf ihres eigenen unzutreffenden Lambda-CDM
Hubble-Diagramms voraus (und zwar ohne jede ausdrückliche
Rechtfertigunng). Deshalb können sie natürlch auch keinen Unterschied
zwischen der lokalen und der universellen Hubble-Konstante finden,
obwohl es im urspünglichen Artikel von Jha, Riess & Kirshner
überzeugend heißt: ''"... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology."'' <ref>S. Jha, A.G. Riess, &
R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere
Literturangaben darin)</ref>

Nun beweist aber das Auftreten zweier verschiener Werte der
Hubble-Konstante das konsistente SUM-Konzept geradezu. Dies zeigt auch,
dass es ebenso andere unerwartete Zusammenhänge geben könnte, die noch
zu entdecken bzw. im Rahmen von SUM zu erklären sind. So scheint es
nicht unmöglchh, auf dieser Bais mit Hilfe von 'high
precision'-Messungen scheinbarer Helligkeiten die Energie-Massen-Dichte
unserer anisotropen kosmischen Nachbarschaft genauer zu ermitteln.

== Vergleich mit den Supernova-Ia-Daten ==
Die zitierte Feststellung von Riess et al. 2011, dass ihr gemessener
Wert von H0 ebenfalls hochgradig inkonsistent ist mit den einfachsten
Modellen inhomogener Materie, die zur Erklärung der scheinbaren
Beschleunigung des Universums ohne 'dunkle Energie' aufgerufen sind
("measured H0 is also highly inconsistent with the simplest
inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"), beruht auf einem populären
Trugschluss indem dabei der fiktive "Big-Bang" als sicheres Szenario von Anfang an einfach vorausgesetzt wird. Tatsächlich aber läßt sich diese
Behauptung duch einen simplen Plot ihrer eigenen SNeIa 'gold'-Daten im
universalen Rotverschiebungsbereich z > 0.1 leicht widerlegen (diese
Widerlegung braucht nicht einmal irgendwelches eigenes
astrophysikalisches Fachwissen, da ihre öffentlich verfügbaren und mit
dem Nobelpreis ausgezeichneten zugrundeliegenden Daten zu Recht als
unanfechtber gelten).

Zur Erklärung der Supernova-Ia-Daten<ref>A.G. Riess et al. (High-z Supernova Search Team), [http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref><ref>M. Kowalski et al. (The Supernova Cosmology
Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> auf
hinreichend großen universalen Skalen benötigt das Modell SUM keine
'dunkle Energie' und unterscheidet sich auch damit vom
[[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Modell]] als dem Standardmodell der gegenwärtigen
[[wikipedia-de:Kosmologie|Kosmologie]]. Abweichungen im Bereich ''z'' < 0.1 werden hier auf
einen lokalen Hubble-Kontrast zurückgeführt, wie er in entsprechender
Größenordnung
tatsächlich beobachtet wurde. Der universale SUM-[[wikipedia-de:Absolute Helligkeit|Entfernungsmodul]] ergibt sich nach bewährter Vorgehensweise
aus dem stationären Linienelement zu
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math> ,
wobei die [[wikipedia-de:Scheinbare Helligkeit|Magnitude]] ''m'' ein Maß für die
[[wikipedia-de:Scheinbare Helligkeit|scheinbare Helligkeit]], und ''M'' einen
geeignet zu wählenden Wert für die [[wikipedia-de:Absolute Helligkeit|absolute Helligkeit]] beispielsweise
von [[wikipedia-de:Supernova vom Typ Ia|Supernovae Typ Ia]] (SNe-Ia) als [[wikipedia-de:Standardkerze|''Standardkerzen'']] darstellt. Das
MG12-Dokument ''Indication from the Supernovae Ia Data of a Stationary
Background Universe''<ref>P. Ostermann,
[http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (sinnvollerweise im pdf-Ganzseitenmodus
durchzublättern)</ref> zeigt die unmittelbare Übereinstimmung des
SUM-Entfernungsmoduls mit den Supernova-Daten für ''universale''
Rotverschiebungswerte ''z'' > 0.1 (erst oberhalb solcher,
größenordnungsmäßig der [[wikipedia-de:Sloan Great Wall|Sloan Great Wall]] entsprechender Skalen kann
das Universum als homogen und isotrop betrachtet werden). Darin geht aus einer Reihe systematisch aufeinanderfolgender Abbildungen auch hervor,
warum zur Vermittlung zwischen den Voraussagen des erwarteten
[[wikipedia-de:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter-Modells]] und denjenigen der alten [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] das Konzept einer die kosmologische Konstante repräsentierenden 'dunklen Energie' notwendig
schien. Wird aber an den originalen
[[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] ohne
[[wikipedia-de:kosmologische Konstante|kosmologische Konstante]] festgehalten, so hätten die SNe-Ia-Messungen das SUM-Linienelement offensichtlich bestätigt. Im Rahmen der
entsprechenden Berechnungen ergibt sich aufgrund universaler
[[wikipedia-de:Rotverschiebung|Rotverschiebung]] und [[wikipedia-de:Zeitdilatation|Zeitdilatation]] selbst bei unendlich vielen
Sternen ein realistischer endlicher Wert für die Helligkeit des
Nachthimmels, so dass das [[wikipedia-de:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olberssche Paradoxon]] auch ohne die Annahme eines Urknalls
oder einer Expansion des Raums hier gelöst ist.

== Alternative zum materiellen Beitrag der 'dunklen Energie' ==
Zusätzlich zu indirekt beobachteten oder durch
[[wikipedia-de:Gravitationslinseneffekt|Gravitationslinseneffekte]] gemessenen
[[wikipedia-de:Inhomogenität|Inhomogenitäten]] sollte es im Rahmen von SUM einen
annähernd homogen verteilten, optisch ebenfalls transparenten Beitrag
einer ''dunklen'' Materie geben, der sich ''nicht'' durch solche
[[wikipedia-de:Gravitationslinseneffekt|Gravitationslinseneffekte]] nachweisen lässt. Dieser homogene Anteil, der im [[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Modell]] einer
''[[wikipedia-de:Dunkle Energie#Beobachtung|dunklen Energie]]'' zugeschrieben wird, könnte hier
die Lücke schließen zwischen der insgesamt beobachteten Materie und der
[[wikipedia-de:Kritische Dichte|kritischen Dichte]], die für ein ''flaches'' Modell
ohne räumliche Krümmung notwendig ist. Gleichzeitig findet eine
[[wikipedia-de:Expansion des Universums|Expansion des Raums]] gemäß SUM nicht statt,
so dass auch in dieser Beziehung wieder keine zusätzliche Energie für
eine Beschleunigung erforderlich ist.

Es ist erwiesenermaßen eine falsche Feststellung in Riess et al. 2011 zu lesen ''"The measured <math>H_0</math> is also highly
inconsistent with the simplest inhomogeneous matter models invoked to
explain the apparent acceleration of the universe without dark energy"'' <ref>A.G. Riess et al.,
[http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"],
ApJ 730, 1-18+1, 2011</ref> (s. Fig. W3 instead).

Zusätzlich sei angemerkt, dass ... It may be remarked, that if dark matter was built in huge parts of
thermalized neutrinos, then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying these hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed to come from z > 1000). A preliminary
assessment on base of relation (82) would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, will make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Mikrowellenhintergrundstrahlung und eine 'dunkle Materie' ==

[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - Die
fettgedruckte durchgezogene schwarze Linie steht für das gesamte
CMB-Spetrum so wiie es im Falle <math>\kappa</math> = 2
tatsächlich beobachtet wird. Die fettgedruckte rote Linie zeigt am
Beispiel einer lokalen Kugel vom Radius <math>\Delta
r^*</math> = 100 Mpc die Emission der hDM-Strahlung wie sie sich
hier ergibt. Zusätzlich zeigen die dünnen durchgezogenen roten Linien die jeweiligen Anteile von innerhalb ''z'' = ''Z'' ''von unten nach oben'' mit ''Z'' = 0.1, 0.2, .. 1.0 in diesem Fall.
]]

Im Rahmen von SUM wird die [[wikipedia-de:Hintergrundstrahlung|Hintergrundstrahlung]] (CMB) zum Teil als
[[wikipedia-de:Wärmestrahlung|Wärmestrahlung]] der ''[[wikipedia-de:Dunkle Materie|'dunklen Materie']]''
gedeutet. Dieses Konzept könnte zwei fundamentale Probleme zugleich
lösen: (a) es gibt keine makroskopische Materieverteilung ohne
Temperatur und Wärmestrahlung; und (b) eine stationäre
Hintergrundstrahlung muss innerhalb des Universums entstanden sein. In
einer zunächst rein mathematischen Ableitung ist es gelungen, aus
[[wikipedia-de:Rotverschiebung|rotverschobenen]] Strahlungsanteilen ein perfektes
[[wikipedia-de:Plancksches Strahlungsgesetz|Planck-Spektrum]] ohne [[wikipedia-de:Urknall|Urknall]]
abzuleiten. Bei einer statistisch mittleren universalen Temperatur
scheinen die [[wikipedia-de:Inhomogenität|Inhomogenitäten]] dieser kalten
''[[wikipedia-de:Wärmestrahlung|Wärmestrahlung]]'' die offensichtlich vorhandenen
[[wikipedia-de:Baryonische akustische Oszillation|akustischen Oszillationen]] der
gesamten Materie widerzuspiegeln, die sich über astronomische Zeiträume
auch hier durch das Wechselspiel von [[wikipedia-de:Gravitation|Gravitation]] und
[[wikipedia-de:Strahlungsdruck|Strahlungsdruck]] ausgebildet hätten. Die Chance einer alternativen
Erklärung der CMB-[[wikipedia-de:Anisotropie|Anisotropien]] im Rahmen von SUM springt beim Vergleich verschiedener Abbildungen, beispielsweise Figure 14-e
von ''N. A. Sharp''<ref>N.A. Sharp,
[http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN
0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref> mit Figure
7(b) von ''C. L. Bennett''<ref>C.L. Bennett et al.,
[http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
oder mit Figure 5 von ''R. Piffaretti''<ref>R. Piffaretti et al.,
[http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>
nahezu ins Auge. Im Gegensatz zum Konzept eines ewigen unendlichen
Universums selbst, scheint die vorläufige Erklärung des
[[wikipedia-de:Planck-Spektrum|Planck-Spektrum]]s im Rahmen von SUM mit Hilfe des
[[wikipedia-de:Sunjajew-Seldowitsch-Effekt|Sunjajew-Seldowitsch-Effekt]]s [[wikipedia-de:Falsifikationismus|falsifizierbar]].
Dieser Effekt<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang,
[http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199,
2006</ref><ref>L.E. Bleem et al.,
[http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''],
ApJS, 216, 27, 2015</ref> sollte sich mit zunehmender Entfernung
abschwächen und ab Rotverschiebungswerten ''z''
><math>\,</math>1 bis auf statistische Fluktuationen
allmählich verschwinden. Bemerkenswerterweise enthalten die
entsprechenden PLANCK-Kataloge <ref>P.A.R. Ade et al. (Planck
Collaboration),
[http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck
Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref> tatsächlich ganz überwiegend Beobachtungen bis etwa zu dieser Grenze.

Es ist jedenfalls nicht länger möglich, in der bloßen Existenz der CMB
Hintergrundstrahlung einen sicheren Beweis für eine Big-Bang Entstehung
des gesamten Universums zu sehen.

== Der alternative Sunyaev-Zel'dovich Effekt ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - Die CMB-Anteile
<math>\rho _Z^*</math>, die gemäß SUM von ''außerhalb'' der
Grenze <math>z = Z</math> kommen. Die durchgezogenen dünnen
roten Linien zeigen dies ''von oben nach unten'' für
<math>Z</math> = 0.1, 0.2, .. 1.0.]]

Der nach Rashid Sunyaev und Yakov Zel’dovich benannte Effekt beschreibt
eine in gewissen Frequenzbereichen leichte Abschwächung der
Hintergrundstrahlung durch Galaxienhaufen. Anders als im
''Konkordanzmodell'' sollte sich dieser Effekt gemäß vorläufiger
Erklärung im Rahmen von SUM mit zunehmender Entfernung abschwächen und
bei Rotverschiebungswerten größer als Eins allmählich verschwinden.
Bemerkenswerterweise enthält der entsprechende Katalog der
PLANCK-2013-Ergebnisse tatsächlich nur Beobachtungen bis etwa zu dieser
Grenze. Im Jahr 2015 wurde tatsäclich ein 'Sunyaev-Zel'dovich prediction cluster count mismatch' konstatiert.

Mit den Planck 2015 Daten und der Möglichkeit einer unvoreingenommenen
neuen Statistik des Sunyaev-Zel'dovich Effekts gibt es nun eine reelle
Chance, endgültig zu entscheiden, ob die CMB Hintergrundstrahlung einst
tatsächlich nach einem 'Big Bang' entstanden ist oder eben nicht: ob sie also stattdessen umgekahrt vom 'dunkler' Materie innerhalb eines
nicht-expandierenden Universums emittiert wird.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - Der realistische SZ-Effekt
zusammen mit einem Beispiel anderer CMB-Verzerrungen wie z.B.
zurück-verschiebender Inhomogenitäten.
-- '''''Obere Abb. (a)''''': Isotherme CMB-Fluktuationen der Ordnung
<math>y</math> ≈ 10^{-4} sind schwach rot gezeichnet,
wohingegen die dünnen gebogenen blauen und grauen Linien Änderungen des
lokalen SZ-Effekts zeigen.
-- '''''Untere Abb. (b)''''': Diese hoch-bedeutsame Abbildung
demonstriert ein resultierendes SZ-Signal als fettgedrucke rote Linie
(<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot
10^{-5}</math>), wobei die gemäß SUM resultierende ''isolierte''
Fequenz-Verschiebung durch solch eine zufällige
Hintergrund-Inhomogenität weitgehend aufgehoben wäre [kleinere
Intensitäten könnten als kleinere Werte der Clustermassen (in y)
interpretiert werden].]]

== Andere Beobachtungstatsachen und offene Fragen ==
Zusätzlich zu den im Rahmen von SUM besonders einfach beschreibbaren
kosmologischen Beobachtungstatsachen von universaler Rotverschiebung und den Supernova-Ia-Helligkeiten, die als zwei fundamentale Stützpfeiler
der [[wikipedia-de:Urknall|Urknall-Theorie]] gelten, scheinen auch weitere
Sachverhalte – bisher allerdings vor allem ansatzweise – alternativ
erklärbar.

* Nukleosynthese – In einem nach Voraussetzung stationären Universum ist der jeweilige Anteil aller materiellen Komponenten dadurch bestimmt, dass diese im Einklang mit den Gesetzen der Quantenmechanik in ''originären'' Prozessen wiederhergestellt werden, und zwar im gleichen Verhältnis, wie sie zuvor in Gravitationszentren extremer Stärke verschwunden sind. Das [[wikipedia-de:Urknall|Urknall]]-Modell benutzt an keiner Stelle, dass es außerhalb des dort ins Auge gefassten Bereichs extremer Temperaturen und Dichten nicht weitere solcher Ereignisse (''multi bangs'') geben könnte. Es kann auch nicht ausgeschlossen werden, dass die Freisetzung von Materie in Form von [[wikipedia-de:Jet (Astronomie)|Jets]] – mitsamt anschließender Bildung von [[wikipedia-de:Plasma|Plasma]]-Blasen – für eine ständige Wiederherstellung [[wikipedia-de:Primordiale Nukleosynthese|primordialer]] Kerne und ihrer Bestandteile sorgen.

* Quasar-Verteilung (und ältere Galaxienformen in großen Entfernungen) – Seit in den 1960er Jahren festgestellt wurde, dass der [[wikipedia-de:Quasar|Quasar]] [[wikipedia-de:3C 273|3C 273]] kein naher Stern ist, sondern mit einer
[[wikipedia-de:Rotverschiebung|Rotverschiebung]] von ''z'' = 0,158 im Bereich ferner Galaxien liegt, wurden in späteren Beobachtungen diese hellen sternartigen Gebilde in sehr viel größeren Entfernungen erkannt. Quasare wurden inzwischen bis zu einer Rotverschiebung von mindestens ''z'' = 7,1 entdeckt, woraus folgt, dass sich die nächsten von ihnen aus heutiger Sicht in kosmischer Nachbarschaft befinden. Selbst eine endgültige Beobachtung, dass sich solche
''[[wikipedia-de:Quasar|''Quasistellaren Objekte]]'' tatsächlich nur in überdurchschnittlichen Entfernungen befänden, wäre eine Selbstverständlichkeit, wenn die Evolution unseres 'lokalen' evolutionären Kosmos in einem ''Multi-Bang''-Ereignis – verträglich mit SUM – ihren Anfang genommen hätte; aus dem gleichen Grund könnten auch die meisten der sehr weit entfernten Galaxien tatsächlich jünger aussehen. Demgegenüber scheint die gemessene Häufigkeitsverteilung von Quasaren derzeit auf sehr großen Skalen ab ''z'' > 2-3 durch [[wikipedia-de:Selbstselektion|Selbstselektionseffekte]] wie dem so genannten ''[[wikipedia-de:Gunnar Malmquist|Malmquist-Bias]]'' zunächst reduziert und dann begrenzt zu sein, wobei alle Objekte unterhalb einer schwachen Helligkeitsgrenze unberücksichtigt bleiben.

* Grundsätzliche SUM-Unterschiede zu einer Urknall-Entstehung aus dem Nichts – Obwohl diverse als ''Säulen'' der [[wikipedia-de:Urknall|Urknall-Kosmologie]] bezeichnete fundamentale Beobachtungstatsachen numerisch glänzend bestätigt sind, bleiben doch wichtige Fragen. Ein ''[[wikipedia-de:Vakuumenergie|falsches Vakuum]]'' von ''[[wikipedia-de:Vakuumfluktuation|Quantenfluktuationen]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref>, wenn unser evolutionärer Kosmos daraus gemäß der [[wikipedia-de:Urknall|Urknall-Theorie]] entstanden wäre, könnte insgesamt nicht ohne Energiedichte gewesen sein, so dass ein solches ''[[wikipedia-de:Tohuwabohu|Tohu-va-bohu]]'' auch als universaler ''[[wikipedia-de:Urknall#chaotische Inflation|chaotischer Hintergrund]]'' der Beschreibung durch [[wikipedia-de:Albert Einstein|Einsteins]]
[[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] bedarf. Außer im Rahmen von SUM scheint eine Lösung nicht vorzuliegen. Hier aber tauchen solche und ähnliche Probleme der
''[[wikipedia-de:Lambda-CDM-Modell|Konkordanzkosmologie]]'' gar nicht auf, oder sie erscheinen in einem anderen Licht.

* Einschränkung des Entropiesatzes auf evolutionäre Prozesse – Bei gravitativen Neuentstehungsprozessen, möglicherweise in supermassereichen Objekten wie [[wikipedia-de:Aktiver Galaxienkern|aktiven Galaxienkernen (AGNs)]],
[[wikipedia-de:Hypernova|Hypernovae]] oder Quellen von [[wikipedia-de:Gammablitz|Gammablitzen]], sollte die [[wikipedia-de:Entropie|Entropie]] in lokalen Bereichen eines ewigen Universums zeitweilig abnehmen, damit sie insgesamt stationär bleiben kann. Dazu bedarf es einer Einschränkung des Gesetzes von der ständigen Zunahme der [[wikipedia-de:Entropie#Zweiter Hauptsatz|Entropie]] auf evolutionäre Prozesse, ohne dass dies einer von Lebewesen gemachten experimentellen Erfahrung jemals widersprechen könnte. Die Notwendigkeit einer vorübergehenden örtlich begrenzten Abnahme der Entropie ist unumgänglich für jedes stationäre Konzept überhaupt (ansonsten wäre ein lange diskutierter
''[[wikipedia-de:Wärmetod (Physik)|Wärmetod des Universums]]'' unvermeidlich). So unwahrscheinlich eine solche Einschränkung aber klingen mag,
so ist sie physikalisch doch weniger unwahrscheinlich als eine Entstehung des gesamten Universums aus dem ''[[wikipedia-de:Inflation (Kosmologie)#Entstehung aus dem Nichts?|Nichts]]''.

Zur Überwindung fundamentaler ''Fine-Tuning''-Probleme der
[[wikipedia-de:Urknall|Urknall-Theorie]], welche die ''Flachheit'' des Universums
oder die Nicht-Existenz ''magnetischer Monopole'' oder dessen
''Horizont'' betreffen, wurde eine Phase ''[[wikipedia-de:Inflation (Kosmologie)|kosmischer Inflation]]'' erdacht. Diese soll von einem
skalaren ''[[wikipedia-de:Inflation (Kosmologie)#Felddynamik| Inflatonfeld]]''
getrieben worden sein, das allerdings niemals experimentell beobachtet
worden ist. Auch die Tatsache der universalen
''[[wikipedia-de:Materie-Antimaterie-Asymmetrie|Materie-Antimaterie-Asymmetrie]]'' ist im Rahmen der gegenwärtig
vorherrschenden Kosmologie mit konkreter experimenteller Erfahrung nicht vereinbar. Ebenso wenig wäre gemäß der ursprünglichen
[[wikipedia-de:Urknall|Urknall-Theorie]] verständlich, dass es seit einer Entstehung
aus dem Nichts überhaupt gleichbleibende Naturgesetze gibt, und nicht
alles Geschehen bis heute nur vollkommen chaotisch abläuft. Irritierend
ist auch die Berufung auf ein ''imperfektes'' [[wikipedia-de:Kosmologisches Prinzip|Kosmologisches Prinzip]], das aus der ansonsten universalen Symmetrie nur die Zeit
willkürlich ausschließt. Das vielleicht größte aller
''Koinzidenz-Probleme'' besteht darin, dass die gewöhnlich als ''Alter
des Universums'' bezeichnete Zeitspanne ''t''0
ausgerechnet heutzutage näherungsweise mit dem Kehrwert der
konventionellen [[wikipedia-de:Hubble-Konstante|Hubble-Konstante]] 1/''H''0
übereinstimmen soll. Das ''[[wikipedia-de:Anthropisches Prinzip|anthropische Prinzip]]'' betrifft gemäß SUM nicht das stationäre Universum selbst,
sondern die möglichen evolutionären Kosmen darin. Durch die inzwischen
erfolgte Erweiterung des [[wikipedia-de:Urknall|Urknall]]-Konzepts – von ursprünglich einem
einzigen ''Big Bang''-Universum über zusätzliche
''[[wikipedia-de:Parallelwelt|Paralleluniversen]]'' bis hin zu einem nun wieder
allumfassenden ''[[wikipedia-de:Parallelwelt|Multiversum]]'' – scheint sich die
Kosmologie schließlich auf das SUM-Konzept mit seiner natürlichen
Unterscheidung des stationären Universums von evolutionären
''Multi-Bang''- bzw. lokalen ''Quasi-Bang''-Kosmen hinzuentwickeln. Es
ist im Zusammenhang mit vermeintlichem Alter und vermuteten Grenzen des
Universums bemerkenswert, dass Vorstellungen darüber immer wieder
erweitert wurden, seit [[wikipedia-de:Immanuel Kant|Immanuel Kant]] in schon damals beobachtbaren
Sternnebeln zum Teil ferne ''[[wikipedia-de:Milchstraße|Milchstraßen]]'' erkannte.

== Zur Vereinbarkeit von Relativitätstheorie und Quantenmechanik ==
In ''Geometrie und Erfahrung''<ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref> hat [[wikipedia-de:Albert Einstein|Albert Einstein]] sechs Jahre nach
Vollendung der [[wikipedia-de:Allgemeine Relativitätstheorie|allgemeinen Relativitätstheorie]] zwei mögliche Deutungen einander gegenübergestellt und dabei [[wikipedia-de:Henri Poincaré|Poincarés]] Auffassung der
[[wikipedia-de:Nichteuklidische Geometrie|nichteuklidischen Geometrie]]<ref>H.
Poincaré, [https://archive.org/details/wissenschaftundh00poin "''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L.
Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice
Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
grundsätzlich anerkannt ("''Sub specie aeterni hat Poincaré mit dieser
Auffassung nach meiner Meinung Recht''"). Demzufolge ist es möglich, die nichteuklidische Geometrie der allgemeinen Relativitätstheorie nicht
Raum und Zeit selbst, sondern gravitativ beeinflussten Maßstäben, Uhren
und allen anderen realen physikalischen Objekten zuzuschreiben und
ansonsten die [[wikipedia-de:Euklidische Geometrie|euklidische Geometrie]] zur
vollständigen Beschreibung des Naturgeschehens beizubehalten. Das
gelingt mit Hilfe einer von [[wikipedia-de:Nathan Rosen|Nathan Rosen]] formulierten ''bimetrischen Relativitätstheorie'' (bi-metric relativity)<ref>N. Rosen,
"''Flat-Space Metric in General Relativity Theory''", Ann. of Physics
22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>. Eine
solche Möglichkeit würde andererseits auch erklären, warum es bisher
trotz großer Anstrengungen ([[wikipedia-de:Stringtheorie|Stringtheorie]],
[[wikipedia-de:Schleifenquantengravitation|Schleifenquantengravitation]]) nicht überzeugend gelungen scheint, die ''[[wikipedia-de:Raumzeit|Raumzeit]]'' zu quantisieren und so die in herkömmlichem Sinne
verstandene [[wikipedia-de:Relativitätstheorie|Relativitätstheorie]] grundsätzlich mit der
[[wikipedia-de:Quantenmechanik|Quantenmechanik]] in einer [[wikipedia-de:allgemeine Relativitätstheorie#Quantenphysik|einheitlichen Theorie von Gravitation und Quantenmechanik]] zu vereinbaren.
Gemäß SUM-Ansatz aber scheint eine Vereinheitlichung prinzipiell möglich, um künftig gültige Aussagen zu
andernfalls bloßen mathematischen [[wikipedia-de:Singularität (Astronomie)|Singularitäten]] der allgemeinen Relativitätstheorie
überhaupt machen zu können, oder wenigstens Fehldeutungen zu verhindern. Dies betrifft neben der Theorie ''[[wikipedia-de:allgemeine Relativitätstheorie#Schwarze Löcher|schwarzer Löcher]]'' auch die
[[wikipedia-de:Singularitäten-Theorem|Singularitätstheoreme]] von [[wikipedia-de:Stephen Hawking|Hawking]] und [[wikipedia-de:Roger Penrose|Penrose]], bei denen in
Ermangelung einer konsistenten Theorie die tatsächliche Quantenstruktur
der Materie bisher außer acht bleiben musste.

== Numerische Hinweise auf die Existenz von 24 elementaren Spin-½ Torsionsteilchen ==

Obwohl mit dem Äquivalenzprinzip in seiner bisherigen Form unvereinbar,
gibt es einen klaren Hinweis auf die Materialisation eines
antisymmetrischen Windungstensors <math>T_{ikl}</math>. Das
Universum scheint demzufolge aus 24 Sorten von Spin-1/2 Partikeln
zusammengesetzt, nämlich aus 6 Arten von Leptonen plus 3 Farben mal 6
Sorten Quarks. Dies entspricht gerade den 24 Komponenten eines
Windungstensors, von denen 6 als 'zeitlich' plus 3*6 als 'räumlich' zu
bezeichnen sind:

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

Schon vor langer Zeit haben Landau & Lifschitz gezeigt, dass die
reale Existenz eines Windungstensors dem Einstein'schen
Äquivalenzprinzip widrsprechen müsste, welches der geometrischen
Interpretation seiner Gravitationsgleichungen zugrundeliegt.
Demgegenüber scheitert der Versuch aus Sicht von SUM, di Physik auf
Riemannsche Eigenschaften einer nicht-Euklidischen 'Raumzeit'
zurückzuführen. Damit scheitert letztlich auch die gesamte
Big-Bang-Kosmologie.

Im Hinblick auf ausgedehnte elementare Spin-1/2-Strukturen (die sich in
den meisten Situationen identfizierbar als ganze verhalten) werden auch
Heisenbergs Unchärferelationen verständlich, ganz im Unterschied zum
Verhalten ansonsten bisher unrealistischerweise vorausgesetzter
'Punkt-Teilchen' wie z.B. Elektronen oder Protonen. Diese sind keine
ausdehnungslosen 'Massen-Punkte' sondern natürlich aausgegdehnte
deformierbare Strukturen mit Teilchen-Parametern in Form konstanter
Integrale für u.a. Spin, Ladung, Ruhemasse. Insbesondere die
quantenmechanische Tatsaache, dass Teilchen im allgemeinen keinen
scharfen Impuls haben, ist angesichts relativer innerer Verschiebungen
ledigkich eine natürliche Feststellung.

Das Torsionskonzept ist unabhängig von der Frage, ob solche Teilchen als materielle Objekte im Vakuum existieren oder in Form von
Wirbelstrukture in einem kontinuierlich ausgedehnten Medium. Die Natur
kann beide Aspekte zeigen (wie bei Spiralnebeln in einem Hintergrund
dunkler Materie).
Die folgende Möglichkeit scheint ''evident'': 
– Elementarteilchen sind Wirbelstrukturen. 
– Aufgrund des Drehimpulserhaltungssatzes sind die winzig
ausgedehnten freien Wirbelstrukturen teilweise über
astronomische Zeiträume beständig. 
– Wirbelstrukturen unterliegen Entstehungs- und
Vergehungsprozessen. 
– In Übergangsphasen verlieren Wirbelstrukturen ihre
Identität. 
– Wirbelstrukturen lassen sich in einer Hinsicht
näherungsweise beschreiben als Teilchen. 
– Wirbelstrukturen lassen sich in anderer Hinsicht
näherungsweise beschreiben als Wellen. 
– In Wirbelstrukturen sind detaillierte Geschwindigkeiten ihrer
Bestandteile und die statistischen Geschwindigkeiten der
jeweiligen Schwerpunktbewegung gleichzeitig realisiert,
woraus sich ganz natürlich Unschärfebeziehungen ergeben. 
Demnach scheinen die Elementarteilchen, aus denen das gesamte Universum
aufgebaut ist, wesentlich verschieden von jenen ewigen festen 'Atomen'
der bahnbrechenden antiken Philosophen Leukipp und Demokrit. Nachdem
klar ist, dass Torsionspartikel nur um den Preis unvermeidlicher
Unschärfen als audehnungslose Punktteilchen behandelt werden dürfen,
muss eine vollständige relativistische Mechanik zukünftig eine
konsistente Formulierung der Quantenmechanik enthalten. Eine geeignete
Basis dafür bietet Rosens 'bi-metrische' Formulierung der
Relativitätstheorie, nachdem sie nun in das (ausgezeichnete) universale
Bezugssystem eingebunden ist.

== Historisches, SUM-Vorläufer, verschiedene verwandte Ansätze ==

Es ist ganz unmöglich, Kosmologie zu betreiben ohne geeignete
Prinzipien, welche - neben der unverzichtberen Verträglichkeit mit
eindeutigen Beobachtungstatsachen - die Kriterien von Einfachheit,
Angemessenheit und Klarheit zu erfüllen haben. Ohne solche Kriterien
wäre gemäß Allgemeiner Relativitätstheorie aufgrund legitimer
Koordinatentransformaionen heute nicht einmal mehr die kopernikanische
Entscheidung zwischen einem heliozentrischen und einem geozentrischen
Planetensystem eindeutig möglich.

Albert Einstein ist bei seiner Begründung der relativistischen
Kosmologie<ref>A. Einstein,
"''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''",
Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref> von der
Voraussetzung eines ewigen Universums ausgegangen. Dieser Versuch ist
daran gescheitert, dass er eine rein ''statische'' Lösung gesucht hat,
deren Linienelement – im Unterschied zu dem Linienelement [[wikipedia-de:Alexander Alexandrowitsch Friedmann|Friedmanns]] wie auch zu demjenigen des
stationären Ansatzes SUM – eine Zeitkoordinate in den entsprechenden
Gravitationspotentialen ''gik'' nicht enthält.
Dies galt auch für die ursprüngliche Form des [[wikipedia-de:De-Sitter-Modell|De-Sitter-Modell]]s, die sich aber durch bloße Koordinatentransformation in das Linienelement
der späteren Steady-State-Theorie überführen ließ.

* Steady-State-Theorie: Unter dem Namen [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]], die eine beständige Expansion beschreiben sollte, wurde im Jahr 1948 ein später (in unterschiedlichen Versionen) an Beobachtungstatsachen gescheitertes Modell des Universums präsentiert, das nach Auffassung seiner Autoren aufgrund ständiger Schöpfung aus dem Nichts als von gleichbleibender Materiedichte erfüllt anzusehen war. Erst in jüngster Zeit wurde bekannt, dass bereits Einstein das Konzept dieser Theorie im wesentlichen vorweggenommen und verworfen hat. Im Unterschied zu SUM wird hier eine ständige Schöpfung aus dem Nichts beschrieben, wobei sich ein von [[wikipedia-de:Fred Hoyle|Fred Hoyle]] eingeführtes ''C''-Feld als Vorläufer des Skalarfeldes des heutigen Inflationsmodells verstehen lässt. Die Rotverschiebungswerte jeweiliger Galaxien ergeben sich in der [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] nicht statistisch konstant, sondern würden entsprechend den zitierten Titeln jener Arbeiten (mit ausdrücklichem Bezug auf ein ''expandierendes Universum'') ständig zunehmen.

* Coasting Cosmology: Ein Modell mit allgemeinerer als der oben angegebenen FLRW-Form des SUM-Linienelements – jedoch mit [[wikipedia-de:Skalenfaktor|Skalenfaktor]] ''HT'' – wurde seinerzeit unter dem Aspekt einer ''gleitenden'' Expansion des Universums diskutiert<ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, bevor 2011 (und später) ein
eng damit verwandtes Konzept noch einmal im Kontext der [[wikipedia-de:Urknall|Urknall-Kosmologie]] behandelt wurde<ref>F. Melia & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct universe''"], MNRAS 419, 2579, 2012</ref>. Beide unterscheiden sich grundsätzlich von SUM (die fundamentale Konsequenz gleichbleibender Rotverschiebungswerte von Quellen in gleichbleibenden universalen Entfernungen wurde nicht erwähnt).

* Chaotic Inflation: Der Physiker [[wikipedia-de:Andrei Dmitrijewitsch Linde|Andrei Linde]] hat das Konzept einer [[wikipedia-de:Urknall#chaotische Inflation|chaotischen Inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> entwickelt und dabei die theoretische Fixierung auf einen einzigen Urknall aus dem Nichts effektiv aufgehoben. Andererseits wird dort von ''Parallel''-Universen gesprochen, wovon jedes mit eigener Inflation und gegebenenfalls eigenen Naturgesetzen entstanden sei. Zu den Grundvoraussetzungen von SUM – viele kosmische Bereiche in einem einzigen Universum mit überall gleichen Naturgesetzen – steht das in klarem Widerspruch. In diesem Zusammenhang (obwohl in völlig anderem mathematischen Kontext) ist auch der Begriff 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> erstmalig aufgetaucht.

Hinsichtlich eines ewig im Wandel befindlichen Universums hat es
offenbar schon immer entsprechende Vorstellungen gegeben. Diese scheinen verwandt zum [[wikipedia-de:Samsara|Kreislauf von Werden und Vergehen]] in östlichen Religionen. Nach Auffassung [[wikipedia-de:Epikur|Epikur]]s existieren in einem unendlich
großen Raum eine unendliche Anzahl von Welten. Darüber wurde von Lukrez
in ''[[wikipedia-de:De rerum natura|Über die Natur der Dinge]]'' berichtet. Gemäß
[[wikipedia-de:Rhazes|Rhazes]] sollen – im Sinne zeitloser Naturgesetze – eine ewige Materie aus Atomen, eine absolute und ewige (im Unterschied zur 'geschaffenen'
Welt aber relative) Zeit sowie ein absoluter und ewiger (im Unterschied
zur 'geschaffenen' Welt aber relativer) Raum unveränderlich vorgegeben
sein. Ähnliche Konzepte von Raum und Zeit finden sich später bei Newton. [[wikipedia-de:Nikolaus von Kues|Nikolaus von Kues]] hat sich eine [[wikipedia-de:Parallelwelt|Vielheit von Welten]] in einem einzigen unbegrenzten Universum gedacht. Die im Sinne
moderner Naturwissenschaft neubelebte Vorstellung eines ewigen
unendlichen [[wikipedia-de:Universum|Universum]]s aber existiert spätestens seit
[[wikipedia-de:Thomas Digges|Thomas Digges]]. Sein Zeitgenosse [[wikipedia-de:Giordano Bruno|Giordano Bruno]] verteidigte die Idee
''vieler Welten'', wie insbesondere aus seiner Schrift ''Über die
Unendlichkeit, das Universum und die Welten'' von 1584 hervorgeht (der
Wortwahl dieses Titels entspricht auch die SUM-Unterscheidung von
''Universum'' und ''Kosmen''). Er hatte dabei die Vorstellung, dass das
[[wikipedia-de:Giordano Bruno#Unendlichkeit des Weltalls|ewige unendliche Universum]] ''von demselben göttlichen Puls durchwirkt'' sei. Sein Denken wurde
von den genannten Vorgängern beeinflusst. Im Rahmen von SUM wurde nun
gezeigt, dass sich entsprechende Konzepte nicht nur mit Einsteins
Gleichungen vereinbaren lassen, sondern sich aus diesen zu ergeben
scheinen. Einerseits wird zwar dieses neue Modell von der
Mainstream-Kosmologie bisher kaum wahrgenommen, doch andererseits
scheint das aktuelle ''Konkordanzmodell'' mit seiner teilweise
hochspekulativen (durch keine experimentelle Erfahrung konkret
begründeten, aber dort unverzichtbaren)
''[[wikipedia-de:Inflation (Kosmologie)|Inflationsphase]]'' bei nicht wenigen Menschen auf
zunehmende Skepsis zu stoßen.

Die Idee von SUM - als der einzigen diskutablen Alternative der
originalen Gravitationsleichungen Einsteins ohne kosmologische Konstante - ist, dass keine univeralen Horizonte die physsikalische Realität
beschränken dürfen. Außerhalb ihrer lokalen Anwendbarkeit erweisen sich
alle Konzepte der Speziellen Relativitätsteorie im Rahmen der
konventionell verstandenen Allgemeinen Relativitätsteorie als
überinterpretiert. Deshalb braucht SUM eine wissenschaftliche Diskussion statt endloser Scheingefechte gegen längst überholte historische
Versuche wie der alten SST. Kosmologische Theorien sind nicht dazu da,
die Natur belehren zu wollen, sondern von ihr zu lernen und sie in
Ehrfurcht und gebotener Bescheidenheit zu beschreiben.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia-de:Kategorie: Kosmologie (Physik)- DEUTSCH|Kategorie: Kosmologie (Physik)- DEUTSCH]] --
[[wikipedia-de:Benutzer:Nimos15|Nimos15]] ([[wikipedia-de:Benutzer Diskussion:Nimos15|Diskussion]]) 12:15, 10 Mar 2018 (CET)

Stationary Universe Model (SUM) - Deutsch

2026-02-21T13:21:32Z

Admin:

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

Das Modell '''SUM''' ('''Stationary Universe Model''') wurde seit 2001 von dem Physiker ''Peter Ostermann'' aus der Voraussetzung eines
ewigen, unendlichen Universums als offenes Projekt (''work in progress'') entwickelt und auf Basis der
originalen [[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]]
[[wikipedia-de:Albert Einstein|Albert Einstein]]s <ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25.
November 1915, 844-847 – (reprint Doc. 25, CPAE Vol.
6)</ref><ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 –
(reprint Doc. 30 CPAE Vol. 6)</ref> ohne [[wikipedia-de:Kosmologische Konstante|Kosmologische Konstante]] als vernünftige Alternative<ref>P. Ostermann,
"''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054,
2002/04</ref> zum numerisch außerordentlich erfolgreichen
[[wikipedia-de:Urknall#Expansion des Universums|Urknallmodell]] phyikalisch
formuliert. Es wurde beim 12. [[wikipedia-de:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]<ref>P.
Ostermann,
"''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.),
Proc. MG12, W.Sci., 1408-1410, 2012;
[http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref><ref>P. Ostermann,
"''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background
Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.),
Proc. MG12, W.Sci., 1373-1375, 2012;
[http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref> in Paris vorgestellt (MG12 2009, zuvor
bei der DPG-Frühjahrstagung<ref>P. Ostermann,
"''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref> 2007
Heidelberg, erste pre-prints bei arXiv.org). Gegenüber dem aufgrund
exzellenter scheinbarer Bestätigungen seit langem vorherrschenden
[[wikipedia-de:Kosmologie|Standard-Modell]] (''Konkordanzmodell'') in Form der
[[wikipedia-de:Inflation (Kosmologie)|inflationären]]
[[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Kosmologie]] stellt SUM auf Basis eines
neuen Linienelements ein Konzept dar, das im Gegensatz zu der trotz
übereinstimmender Motivation überholten [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] mit
aktuellen kosmologischen Beobachtungstatsachen vereinbar scheint. Trotz
verblüffender Erfolge hat das Modell hinsichtlich diverser Details nicht innerhalb weniger Jahre den hochentwickelten Stand der nahezu
ausgereiften Konkordanzkosmologie erreichen können, sondern befindet
sich noch in einer Anfangsphase; es versteht sich als Ermutigung im
Sinne der ''Aufklärung'': "sapere aude!" (wage zu denken).

<div style="color:red">
Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allowing for the solution of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.
</div>

Das neue kosmologische Modell SUM eines stationären
Hintergrund-Universums beinhaltet keine [[wikipedia-de:Expansion des Universums|Expansion des Raums]]. Es geht aus von der physikalischen
Tatsache, dass aus Nichts nichts entsteht. Das [[wikipedia-de:Weltall|Weltall]] wird als eine insgesamt beständige Gegebenheit betrachtet und im Sinne des
''stationären'' – nicht aber statischen – ''Universums'' von unserem
''[[wikipedia-de:Urknall|evolutionären Kosmos]]'' unterschieden. Alter und Ausdehnung des Universum sind demzufolge unendlich, nicht aber unser Kosmos als
Teil davon.

Was sonst als 'Alter des Universums' bezeichnet wird, stellt sich aus
Sicht von SUM heraus als das Höchstalter makroskopischer Strukturen wie
dem von Sternen, Galaxien, (Super-)Cluster gegebenenfalls bis hin zu dem Höchstalter ganzer Kosmen. Scheinbar gegenteilige Beobachtungen
ältester Galaxien könnnen von einem einzigen gemeinsamen Ursprung nicht
überzeugen. Dies steht in Analogie zu der alltäglichen Erfahrung, dass
das Höchstalter individueller Menschen nicht etwa das Alter der gesamten Population beweist. Im Unterschied zur natürlichen Suche nach der
vitalen Vergangenheit unseres evolutionären Kosmos macht es keinen Sinnnnach einer historischen Entwicklung des ewigen Universums zu fragen.

Trotz gemeinsamer Voraussetzung des ''[[wikipedia-de:Kosmologisches Prinzip|perfekten kosmologischen Prinzips]]'' unterscheidet sich das Model SUM mit statistisch konstanten Werten der [[wikipedia-de:Rotverschiebung|Rotverschiebung]] kosmischer
Strahlungsquellen fundamental von der [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] eines
expandierenden Universums<ref>H. Bondi & T. Gold,
[http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref><ref>F. Hoyle,
[http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical
Society, vol. 108, 372-382, 1948</ref>. Die mathematisch exakt
abgeleiteten gleichbleibenden SUM-Rotverschiebungswerte entsprechen den
nach Voraussetzung statistisch gleichbleibenden [[wikipedia-de:Euklidische Geometrie|euklidischen]] Entfernungen in ''universalen Koordinaten'',
die aus historischen Gründen auch als ''[[wikipedia-de:Entfernungsmaß#Mitbewegte Entfernung|mitbewegt]]'' bezeichnet werden (''comoving coordinates'').
Nach einer zunächst rein mathematischen Ableitung der ''stationären''
[[wikipedia-de:Hintergrundstrahlung|Hintergrundstrahlung]] mit [[wikipedia-de:Plancksches Strahlungsgesetz|Planck-Spektrum]] (ohne Zurückführung auf einen
[[wikipedia-de:Urknall|Urknall]]) wurde eine SUM-Vorgängerversion<ref>P. Ostermann,
"''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''",
arXiv:astro-ph/0312655v6, 2013</ref> weiterentwickelt und zu
''Model of a Stationary Background Universe Behind Our Cosmos'' (2013)
ausgebaut. - Sämtliche zugrunde liegenden Arbeiten stehen auf
[http://independent-research.org "independent-research.org"] zum
Download bereit.

== Das stationäre Linienelement ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – Die
Zuordnungen (<math>\Omega_\mathrm{M}</math>, <math>
w_\mathrm{M} </math>,
<math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0,
0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') =
\mathrm{e}^{Ht'}</math> [obere graue durchgezogene Linie], eine
erste Alternative zu <math>a_\mathrm{CCM}(t')</math> mit
größerem Wert <math>\Omega_\mathrm{\Lambda}</math>) [blaue
gestrichelte Linie], das heutige Concordance Model
<math>a_\mathrm{CCM}(t')</math> [blaue durchgezogene Linie], das stationäre ultra-large scale Universum
<math>a_\mathrm{SUM}(t') = HT'</math> =
<math>1+Ht'</math> [rote gerade Linie], eine zweite Variante zu <math>a_\mathrm{CCM}(t')</math> mit kleinerem Wert
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken
line], das Einstein-de-Sitter Modell <math>a_\mathrm{EdS}(t') =
</math> <math>(1 +
\mathrm{3/2}Ht')^\mathrm{2/3}</math> [untere graue durchgezögene
Linie, favorisiert vor dem SNe-Ia Durchbruch]. Im Kontrast zu anderen
vergleichbaren Werten scheinen die CCM best-fit Parameter
<math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid
line) festgelegt durch die Bedingung, dass ihre Linie den
SUM-Skalenfaktor (rot) an seinen 'Grenzen', d.h. bei HT' = -1 und bei
Ht' ≈ 0 heute treffen sollte. ]]

Im Unterschied zu ''statisch'' besagt ''stationär'', dass ein Zustand
insgesamt gleich bleibt, obwohl sich einzelne Bestandteile ständig
verändern können. Dem Konzept SUM liegt, anders als bei der
''[[wikipedia-de:Induktion (Philosophie)|induktiven]]'' Entwicklung der
[[wikipedia-de:Urknall|Urknall-Kosmologie]], ein ''[[wikipedia-de:Deduktion|deduktiver]]'' Ansatz
zugrunde. Dabei genügen zwei [[wikipedia-de:Postulat|Postulate]], um das hier
zugrundeliegende stationäre [[wikipedia-de:Metrischer Tensor#Linienelement|Linienelement]] abzuleiten:

* Postulat I – In Bezug auf hinreichend große Skalen ist das Universum stationär, homogen und isotrop;
* Postulat II – Abgesehen von lokalen Abweichungen ist die universale Lichtgeschwindigkeit ''c''* = ''c'' .

Aus diesen beiden außerordentlich einfachen Postulaten ergibt sich das
SUM-Linienelement d''σ''*SUM eines räumlich
''flachen'', nicht leeren Universums eindeutig zu:
<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math> .
Hier steht ''H'' für eine wahre ''Hubble-Konstante'' (die im Unterschied zum zeitabhängigen ''konventionellen'' [[wikipedia-de:Hubble-Konstante#Definition|Hubble-Parameter]] ''H''0 der
[[wikipedia-de:Urknall|Urknall-Kosmologie]] als ''signifikant'' bezeichnet wird); die Abkürzung d''σ''*SRT steht für das Linienelement der [[wikipedia-de:Spezielle Relativitätstheorie|speziellen Relativitätstheorie]],
wobei das zusätzliche Symbol
'<math>\,</math>*<math>\,</math>' bei jedem
Auftreten auf die Besonderheit hinweist , dass sich die entsprechenden
Größen auf ''universale Koordinaten'' beziehen (neben den
'[[wikipedia-de:Entfernungsmaß#Mitbewegte Entfernung|mitbewegten Koordinaten]]'
''l''<math>\,</math>* auch die 'konforme Zeit'
''t''<math>\,</math>*). Gemäß SUM stimmen die universalen
Koordinaten immer wieder vorübergehend überein mit den ''[[wikipedia-de:Umgebung (Mathematik)|lokalen]]'' [[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlängen]] und
[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeiten]] der speziellen
Relativitätstheorie. Aus dem ausgeschriebenen Quadrat des Linienelements ist die Konstanz der universalen [[wikipedia-de:Lichtgeschwindigkeit|Lichtgeschwindigkeit]] mit c* ≡
d''l''<math>\,</math>*/d''t'' * = c (für
d''σ''*SUM = 0) sofort ersichtlich. Das
SUM-Linienelement hat weitere bemerkenswerte Eigenschaften.

== Rotverschiebung und signifikante Hubble-Konstante ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - Die SUM
Voraussage des im Rahmen der Lambda-CDM 'big-bang' Kosmologie völlig
unverständlichen Hubble-Kontrasts. -
Zwei verschieden Werte für die Hubble 'Kostante'
<math>H_{\mathrm{local}}</math> =
<math>H_{\mathrm{CCM}}</math> und
<math>H_{\mathrm{universal}}</math> =
<math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:'''''
Die blaue durchgezogene Linie repräsentiert die realen Werte
<math>z_{\mathrm{observed}}</math> der SNe-Ia-Messungen, die rote unterbrochene SUM Linie vernachlässigt mögliche 'peculiar flows' oder lokale Inhomogenitäten. Die maximale Abweichung <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c innerhalb
<math>z</math> < 0.027 entspricht einem maximalen
Kontrast <math>H_{\mathrm{local}}</math> /
<math>H_{\mathrm{universal}}</math> - 1} von ungefähr 9% an
diesem Punkt wo <math>H_{\mathrm{universal}}</math> ≈ 67
km/s/Mpc.

'''''-- Bottom panel (b)}:'''''
Innerhalb <math>r^* < 110</math> Mpc entspricht die blaus Linie <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc,
wohingegen der mittlere Wert in der Übergangszone (bis
<math>z</math> ≈ 0.13) ungefähr
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc beträgt. Die
Differenz führt von
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈
4.7% bis zu
<math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% und entspricht annähernd gerade dem Bereich des lokalen
Hubble-Kontrasts von 6.5% ± 1.8%., wie er von Jha, Riess & Kirshner
berichtet wird}.
]]

Es ist einfach falsch zu behaupten, dass die kosmische Rotverschiebung
eine Expansion des Universums beweist.
Die ''universale Rotverschiebung'' des Lichts entfernter
[[wikipedia-de:Galaxie|Galaxien]] und anderer Strukturen wird im Rahmen von SUM nicht als [[wikipedia-de:Doppler-Effekt|Doppler-Effekt]], sondern im Sinne einer erweiterten
Einsteinschen [[wikipedia-de:Rotverschiebung#Gravitative Rot- und Blauverschiebung|Gravitationsrotverschiebung]] verstanden, woraus sich
wie auch beim Experiment von [[wikipedia-de:Pound-Rebka-Experiment|Pound und Rebka]]
keine Fluchtbewegung zwischen Quelle und Empfänger ergibt (bereits
[[wikipedia-de:Edwin Hubble|Edwin Hubble]]<ref>E.P. Hubble,
[http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N.
Acad. Sci. 15, 168-173, 1929</ref> hatte eine solche Möglichkeit
in Betracht gezogen). Der Unterschied zur gewöhnlichen
[[wikipedia-de:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitativen Rot- und Blauverschiebung]] liegt hier darin, dass es sich im Falle von
SUM um ein ''zeitabhängiges'' Potential handelt, das sich aufgrund des
Vorzeichens immer als ''Rotverschiebung'' auswirkt. Aus der allgemeinen
Definition des [[wikipedia-de:Rotverschiebung|Rotverschiebungsparameters]]
''z'' =
''λ''<math>\,</math>beobachtet /
''λ''<math>\,</math>ausgestrahlt – 1
ergeben sich bei SUM mit
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
solche Werte, die mit der ''signifikanten'' Hubble-Konstante ''H''
unabhängig sind von der Zeit. Diese Werte gelten für Galaxien und alle
kosmologischen Strukturen, die sich in Bezug auf universale Koordinaten
(''x''*, ''y''*, ''z''*) nach Voraussetzung statistisch in Ruhe befinden (die Unabhängigkeit von der Zeit gilt auch für alle anderen Größen, die sich als Funktion der Rotverschiebung ''z'' schreiben lassen).
Insbesondere bedeutet deren Zeitunabhängigkeit, dass zusätzlich zu den
lokalen [[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlängen]] der SRT
nun auch den universalen Entfernungen
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
wegen gleichbleibender Rotverschiebungen entsprechender Objekte eine
reale, physikalisch messbare Bedeutung zukommt. Im Gegensatz zur
[[wikipedia-de:Urknall|Urknall-Theorie]] stellt die universale Entfernung ''l''* im
Rahmen von SUM also eine selbständige – obwohl indirekte – Messgröße
dar.

== Universale Zeit ''t''<math>\,</math>* und die Grenzen von Eigenlänge und Eigenzeit ==
Wegen der exponentiellen Form des Zeitskalars e''Ht'' * hängen relative zeitliche Änderungen e''Ht'' */ e''Ht''o* =
e''H''(''t'' *– ''t''o*) allein ab von
''Differenzen'' Δ<math>\,</math>''t'' * = ''t'' * – ''t''0*. Der gleiche Sachverhalt erlaubt es auch, für beliebige zusammenhängende Ereignisse (dies betrifft insbesondere auch [[wikipedia-de:Spontane Emission|Emission]] und spätere [[wikipedia-de:Absorption (Physik)|Absorption]] von Photonen) den universalen zeitlichen
Anfangspunkt jeweils ''t''0* = 0 zu setzen. Im
Unterschied zur jeweiligen lokalen ''Quasi-Eigenzeit'' ''t'' ' = ''T'' ' – ''T''H (mit der [[wikipedia-de:Hubble-Zeit|Hubble-Zeit]] ''T''H = 1/''H'') ist kein spezieller Punkt der universalen Zeitskala ''t''<math>\,</math>* ausgezeichnet.
Die universale Zeit hat weder Anfang noch Ende. Gemäß dem Linienelement
der in begrenzten Bereichen überall und immer wieder lokal gültig
bleibenden speziellen Relativitätstheorie
(d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) sind
die Intervalle von ''[[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlänge]]'' und
''[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeit]]'' stets miteinander gemeinsam
definiert. Wie daraus mathematisch folgt, können die sich in Bezug auf
das SUM-Linienelement ergebenden Näherungen
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
nur innerhalb lokal begrenzter Bereiche
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
des unendlichen euklidischen Raums (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2) jeweils
vorübergehend Gültigkeit beanspruchen (''R''H =
''c''/''H'' ist der [[wikipedia-de:Beobachtbares Universum#Hubble-Radius|Hubble-Radius]]). Gleiches gilt für alle
SRT-Konzepte überhaupt. Bei uneingeschränkter Gleichheit in den obigen
Näherungen aber würde das SUM-Linienelement in dasjenige der SRT übergehen, und der resultierende Einstein-Tensor würde unzulässigerweise verschwinden (was einer universalen Energiedichte Null und damit einem
leeren Universum entspräche). Diese Zusammenhänge ergeben sich aus einer zweifachen [[wikipedia-de:Koordinatentransformation|Koordinatentransformation]] ''t'' * =
ln<math>\,</math>(''HT''
')<math>\,</math>/<math>\,</math>''H'' und ''l'' * = ''l''
'<math>\,</math>/<math>\,</math>(''HT'' '),
wobei ''T'' ' näherungsweise einer ''Eigenzeit'' entspricht, die nach
obiger Ungleichung jeweils örtlich eingeschränkt ist.

== Die FLRW-Form des SUM-Linienelements ==
Wird nur die universale Zeit ''t'' * gemäß der ersten der beiden oben
angegebenen Formeln transformiert, so folgt das stationäre Linienelement in einer
[[wikipedia-de:Friedmann-Lemaître-Robertson-Walker-Metrik|Friedmann-Lemaître-Robertson-Walker-Form (FLRW-Form)]], und zwar mit dem einfachsten aller in Frage kommenden
[[wikipedia-de:Skalenfaktor|Skalenfaktor]]en
''a''<math>\,</math>SUM = ''HT'' ' zu

:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math> ,
ohne dass sich damit an den physikalischen Tatsachen etwas ändert. Es
lässt sich z.B. leicht verifizieren, dass der zeitunabhängige
SUM-Zusammenhang zwischen der Rotverschiebung ''z'' und der universalen
Entfernung ''l''<math>\,</math>* auch gemäß dieser FLRW-Form bestehen bleibt. Es ist im Hinblick auf die gesamte SUM-Kosmologie von
entscheidender Bedeutung, dass sich die auftretende
'Anfangs'-Singularität der örtlich eingeschränkten ''Quasi-Eigenzeit T'' ' = 0 nur auf lokale Bereiche bezieht und keineswegs ein Alter des
gesamten Universums darstellt. Stattdessen bedeutet sie, wie oben
gezeigt, eine jeweils auf ''l''<math>\,</math>* <
''R''H eingeschränkte maximale Lebensdauer
räumlich begrenzter evolutionärer Strukturen (in Bezug auf die
universale Zeitkoordinate entspricht ''T'' ' = 0 dabei ''t'' * = –oo.

== Energiedichte und negativer Gravitationsdruck ==
Die bei SUM offenbar der ''universalen Energiedichte'' entsprechende
Komponente ''G''00 des [[wikipedia-de:Tensor#Ko- und Kontravarianz|''kovarianten'']]
[[wikipedia-de:Friedmann-Gleichung#Herleitung|Einstein-Tensor]]s ist zeitlich
konstant. Demgegenüber scheint die [[wikipedia-de:Krummlinige Koordinaten#Tensoren zweiter Stufe|gemischt ko- kontravariante]] Komponente
''G''00, die bei Anwendung der [[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] auf lokale [[wikipedia-de:Ideale Flüssigkeit|perfekte Flüssigkeiten]] der
[[wikipedia-de:Phänomenologie|''phänomenologisch'']]''en'' Energiedichte entspräche,
abhängig von der ''universalen Zeit t''<math>\,</math>*.
Dass aber eine solche Abhängigkeit über beliebig große universale
Zeiträume im Unterschied zu lokal begrenzten
[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeiten]] ''t'' unrealistisch wäre, folgt wieder aus der Tatsache, dass kein spezieller Anfangspunkt der
Zeitskala ''t''<math>\,</math>* existiert.

Aus dem SUM-Linienelement ergibt sich zu jedem willkürlich wählbaren
universalen zeitlichen Anfangspunkt ''t''0* = 0
ein negativer Gravitationsdruck von –1/3 der ''[[wikipedia-de:kritische Dichte|kritischen Dichte]]'', dessen Existenz hier sofort einleuchtet.
Im Unterschied zu gewöhnlichen Teilchen in einem Kasten (die sich ohne
dessen Wände aufgrund ihres positiven Drucks sofort
[[wikipedia-de:Diffusion|zerstreuen]]) würden Galaxien innerhalb eines begrenzten
Bereichs des stationären Universums ohne negativen Gravitationsdruck (verursacht vom Gravitationspotential der Materie und Energie außerhalb) zusammenklumpen, was in Bezug auf hinreichend große Skalen nach
Voraussetzung nicht geschehen kann.

== SUM Vorhersage zweier verschiedener Werte für die lokale und die universelle Hubble-Konstante ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Links (a)-(e)''''': Der Vergleich der SUM magnitude-redshift Voraussage (für ''κ'' = 0) mit den original SNe-Ia Daten und der CCM-Voraussage zeigt eine unmittelbare SUM-Übereinstimmung auf universalen Skalen z > 0.1, auf denen das Universum am ehesten zu Recht als homogen und isotrop betrachtet werden darf. Die rote SUM-Linie fällt beinahe vollständig mit der blauen CCM-Linie zusammen (trotz - oder: wegen - der gegenüber der lokalen um 9% höheren ''universalen'' Hubble-Konstante).
 -- '''''Intermediate panels (b),(d)''''': Mit
dem in Abb. W2 gezeigten lokalen Hubble-Kontrast existiert nun eine
volle SUM-Übereinstimmung nicht nuur mit den SNe-Ia Daten des 'High-z
Supernova Search Teams' (Riess et al.) sondern auch mit Kowalskis 2008
Union 'world' Zusammenstellung des 'Supernova Cosmology Projects'
(Perlmutter et al.).
Offensichtlich genügen die Korrekturen von maximal <math>\mathrm
\delta z </math> ≈ 0.002 im Bereich <math>z {\mathrm{observed}}</math> < 0.027 für eine befriedigende
Übereinstimmung von SUM mit den Daten
im Falle des lokalen Hubble-Kontrasts
analog W2 auch im Bereich jeweils kleiner Rotverschiebungswerte.
 -- '''''Lower panels (c),(e)''''': In diesen CCM-Abbildungen sind die
blau-gestrichelten geraden Linien nach der Methode der kleinsten
quadratischen Abweichungen bestimmt und sollten sich im Idealfall als
kongruent zur jeweiligen z-Achse erweisen.
: ]]

In beiden Teilen der Abbilddung W2 repräsentieren die blauen
duchgezogenen Linien die realen SNe-Ia Messungen, wohingegen die
gebrochenen roten Linien (jeweils darunter) für SUM stehen. Eine
maxiimale Abweichhung <math> \mathrm \delta z </math> ≈
0.002 entspricht einem maximalen Huble-Kontrast von ≈+9%. Mit
<math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc würde das
<math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc innerhalb
<math> \mathrm{r^{\ast}}</math> < 110 Mpc
<math>(\mathrm \delta z </math> < 0.027) bedeuten,
während sich der Mittelwert in der Übergangszone gerade auf ungefähr
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc beläuft.

Nun wurde kürzlich von Riess als zweitem der zitierten Autoren ein
"lokaler Wert" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc
berichtet<ref>A.G. Riess et al.,
[http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ
826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]],
[http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
mit einer Toleranz von nur 2.4% (sowie 71.9 km/s/Mpc ±3.8%, was
annähernd übereinstimmt mit 72.8 km/s/Mpc ±3.3% in Bonvin e al.
<ref>V. Bonvin et al.,
[http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790
"arXiv:1607.01790]" </ref>.
Nahe bei Freedman's Wert von 72 km/s/Mpc
<ref>W. L. Freedman et al.,
[http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
aber in klarem Kontrast zu den von der
Lambda-CDM Kosmologie gemäß der neuen Planck 'high-redshift'-Messungen
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
vorausgesagten 67 km/s/Mpc – oder auch anähernd zu den 68 km/s/Mpc von
Cheng Cheng \& Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801
</ref>
bedeutet das ausgerechnet wieder einen Hubble-Kontrast von etwa +9%,
welcher Wert beinahe perfekt mit der original SUM-Vorhersage von 2007
übereinstimmt.

Anscheinend setzen die Autoren Riess et al. des neuen Reports zu Unrecht den gekümmmten Verlauf ihres eigenen unzutreffenden Lambda-CDM
Hubble-Diagramms voraus (und zwar ohne jede ausdrückliche
Rechtfertigunng). Deshalb können sie natürlch auch keinen Unterschied
zwischen der lokalen und der universellen Hubble-Konstante finden,
obwohl es im urspünglichen Artikel von Jha, Riess & Kirshner
überzeugend heißt: ''"... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology."'' <ref>S. Jha, A.G. Riess, &
R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere
Literturangaben darin)</ref>

Nun beweist aber das Auftreten zweier verschiener Werte der
Hubble-Konstante das konsistente SUM-Konzept geradezu. Dies zeigt auch,
dass es ebenso andere unerwartete Zusammenhänge geben könnte, die noch
zu entdecken bzw. im Rahmen von SUM zu erklären sind. So scheint es
nicht unmöglchh, auf dieser Bais mit Hilfe von 'high
precision'-Messungen scheinbarer Helligkeiten die Energie-Massen-Dichte
unserer anisotropen kosmischen Nachbarschaft genauer zu ermitteln.

== Vergleich mit den Supernova-Ia-Daten ==
Die zitierte Feststellung von Riess et al. 2011, dass ihr gemessener
Wert von H0 ebenfalls hochgradig inkonsistent ist mit den einfachsten
Modellen inhomogener Materie, die zur Erklärung der scheinbaren
Beschleunigung des Universums ohne 'dunkle Energie' aufgerufen sind
("measured H0 is also highly inconsistent with the simplest
inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"), beruht auf einem populären
Trugschluss indem dabei der fiktive "Big-Bang" als sicheres Szenario von Anfang an einfach vorausgesetzt wird. Tatsächlich aber läßt sich diese
Behauptung duch einen simplen Plot ihrer eigenen SNeIa 'gold'-Daten im
universalen Rotverschiebungsbereich z > 0.1 leicht widerlegen (diese
Widerlegung braucht nicht einmal irgendwelches eigenes
astrophysikalisches Fachwissen, da ihre öffentlich verfügbaren und mit
dem Nobelpreis ausgezeichneten zugrundeliegenden Daten zu Recht als
unanfechtber gelten).

Zur Erklärung der Supernova-Ia-Daten<ref>A.G. Riess et al. (High-z Supernova Search Team), [http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref><ref>M. Kowalski et al. (The Supernova Cosmology
Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> auf
hinreichend großen universalen Skalen benötigt das Modell SUM keine
'dunkle Energie' und unterscheidet sich auch damit vom
[[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Modell]] als dem Standardmodell der gegenwärtigen
[[wikipedia-de:Kosmologie|Kosmologie]]. Abweichungen im Bereich ''z'' < 0.1 werden hier auf
einen lokalen Hubble-Kontrast zurückgeführt, wie er in entsprechender
Größenordnung
tatsächlich beobachtet wurde. Der universale SUM-[[wikipedia-de:Absolute Helligkeit|Entfernungsmodul]] ergibt sich nach bewährter Vorgehensweise
aus dem stationären Linienelement zu
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math> ,
wobei die [[wikipedia-de:Scheinbare Helligkeit|Magnitude]] ''m'' ein Maß für die
[[wikipedia-de:Scheinbare Helligkeit|scheinbare Helligkeit]], und ''M'' einen
geeignet zu wählenden Wert für die [[wikipedia-de:Absolute Helligkeit|absolute Helligkeit]] beispielsweise
von [[wikipedia-de:Supernova vom Typ Ia|Supernovae Typ Ia]] (SNe-Ia) als [[wikipedia-de:Standardkerze|''Standardkerzen'']] darstellt. Das
MG12-Dokument ''Indication from the Supernovae Ia Data of a Stationary
Background Universe''<ref>P. Ostermann,
[http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (sinnvollerweise im pdf-Ganzseitenmodus
durchzublättern)</ref> zeigt die unmittelbare Übereinstimmung des
SUM-Entfernungsmoduls mit den Supernova-Daten für ''universale''
Rotverschiebungswerte ''z'' > 0.1 (erst oberhalb solcher,
größenordnungsmäßig der [[wikipedia-de:Sloan Great Wall|Sloan Great Wall]] entsprechender Skalen kann
das Universum als homogen und isotrop betrachtet werden). Darin geht aus einer Reihe systematisch aufeinanderfolgender Abbildungen auch hervor,
warum zur Vermittlung zwischen den Voraussagen des erwarteten
[[wikipedia-de:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter-Modells]] und denjenigen der alten [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] das Konzept einer die kosmologische Konstante repräsentierenden 'dunklen Energie' notwendig
schien. Wird aber an den originalen
[[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] ohne
[[wikipedia-de:kosmologische Konstante|kosmologische Konstante]] festgehalten, so hätten die SNe-Ia-Messungen das SUM-Linienelement offensichtlich bestätigt. Im Rahmen der
entsprechenden Berechnungen ergibt sich aufgrund universaler
[[wikipedia-de:Rotverschiebung|Rotverschiebung]] und [[wikipedia-de:Zeitdilatation|Zeitdilatation]] selbst bei unendlich vielen
Sternen ein realistischer endlicher Wert für die Helligkeit des
Nachthimmels, so dass das [[wikipedia-de:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olberssche Paradoxon]] auch ohne die Annahme eines Urknalls
oder einer Expansion des Raums hier gelöst ist.

== Alternative zum materiellen Beitrag der 'dunklen Energie' ==
Zusätzlich zu indirekt beobachteten oder durch
[[wikipedia-de:Gravitationslinseneffekt|Gravitationslinseneffekte]] gemessenen
[[wikipedia-de:Inhomogenität|Inhomogenitäten]] sollte es im Rahmen von SUM einen
annähernd homogen verteilten, optisch ebenfalls transparenten Beitrag
einer ''dunklen'' Materie geben, der sich ''nicht'' durch solche
[[wikipedia-de:Gravitationslinseneffekt|Gravitationslinseneffekte]] nachweisen lässt. Dieser homogene Anteil, der im [[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Modell]] einer
''[[wikipedia-de:Dunkle Energie#Beobachtung|dunklen Energie]]'' zugeschrieben wird, könnte hier
die Lücke schließen zwischen der insgesamt beobachteten Materie und der
[[wikipedia-de:Kritische Dichte|kritischen Dichte]], die für ein ''flaches'' Modell
ohne räumliche Krümmung notwendig ist. Gleichzeitig findet eine
[[wikipedia-de:Expansion des Universums|Expansion des Raums]] gemäß SUM nicht statt,
so dass auch in dieser Beziehung wieder keine zusätzliche Energie für
eine Beschleunigung erforderlich ist.

Es ist erwiesenermaßen eine falsche Feststellung in Riess et al. 2011 zu lesen ''"The measured <math>H_0</math> is also highly
inconsistent with the simplest inhomogeneous matter models invoked to
explain the apparent acceleration of the universe without dark energy"'' <ref>A.G. Riess et al.,
[http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"],
ApJ 730, 1-18+1, 2011</ref> (s. Fig. W3 instead).

Zusätzlich sei angemerkt, dass ... It may be remarked, that if dark matter was built in huge parts of
thermalized neutrinos, then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying these hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed to come from z > 1000). A preliminary
assessment on base of relation (82) would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, will make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Mikrowellenhintergrundstrahlung und eine 'dunkle Materie' ==

[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - Die
fettgedruckte durchgezogene schwarze Linie steht für das gesamte
CMB-Spetrum so wiie es im Falle <math>\kappa</math> = 2
tatsächlich beobachtet wird. Die fettgedruckte rote Linie zeigt am
Beispiel einer lokalen Kugel vom Radius <math>\Delta
r^*</math> = 100 Mpc die Emission der hDM-Strahlung wie sie sich
hier ergibt. Zusätzlich zeigen die dünnen durchgezogenen roten Linien die jeweiligen Anteile von innerhalb ''z'' = ''Z'' ''von unten nach oben'' mit ''Z'' = 0.1, 0.2, .. 1.0 in diesem Fall.
]]

Im Rahmen von SUM wird die [[wikipedia-de:Hintergrundstrahlung|Hintergrundstrahlung]] (CMB) zum Teil als
[[wikipedia-de:Wärmestrahlung|Wärmestrahlung]] der ''[[wikipedia-de:Dunkle Materie|'dunklen Materie']]''
gedeutet. Dieses Konzept könnte zwei fundamentale Probleme zugleich
lösen: (a) es gibt keine makroskopische Materieverteilung ohne
Temperatur und Wärmestrahlung; und (b) eine stationäre
Hintergrundstrahlung muss innerhalb des Universums entstanden sein. In
einer zunächst rein mathematischen Ableitung ist es gelungen, aus
[[wikipedia-de:Rotverschiebung|rotverschobenen]] Strahlungsanteilen ein perfektes
[[wikipedia-de:Plancksches Strahlungsgesetz|Planck-Spektrum]] ohne [[wikipedia-de:Urknall|Urknall]]
abzuleiten. Bei einer statistisch mittleren universalen Temperatur
scheinen die [[wikipedia-de:Inhomogenität|Inhomogenitäten]] dieser kalten
''[[wikipedia-de:Wärmestrahlung|Wärmestrahlung]]'' die offensichtlich vorhandenen
[[wikipedia-de:Baryonische akustische Oszillation|akustischen Oszillationen]] der
gesamten Materie widerzuspiegeln, die sich über astronomische Zeiträume
auch hier durch das Wechselspiel von [[wikipedia-de:Gravitation|Gravitation]] und
[[wikipedia-de:Strahlungsdruck|Strahlungsdruck]] ausgebildet hätten. Die Chance einer alternativen
Erklärung der CMB-[[wikipedia-de:Anisotropie|Anisotropien]] im Rahmen von SUM springt beim Vergleich verschiedener Abbildungen, beispielsweise Figure 14-e
von ''N. A. Sharp''<ref>N.A. Sharp,
[http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN
0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref> mit Figure
7(b) von ''C. L. Bennett''<ref>C.L. Bennett et al.,
[http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
oder mit Figure 5 von ''R. Piffaretti''<ref>R. Piffaretti et al.,
[http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>
nahezu ins Auge. Im Gegensatz zum Konzept eines ewigen unendlichen
Universums selbst, scheint die vorläufige Erklärung des
[[wikipedia-de:Planck-Spektrum|Planck-Spektrum]]s im Rahmen von SUM mit Hilfe des
[[wikipedia-de:Sunjajew-Seldowitsch-Effekt|Sunjajew-Seldowitsch-Effekt]]s [[wikipedia-de:Falsifikationismus|falsifizierbar]].
Dieser Effekt<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang,
[http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199,
2006</ref><ref>L.E. Bleem et al.,
[http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''],
ApJS, 216, 27, 2015</ref> sollte sich mit zunehmender Entfernung
abschwächen und ab Rotverschiebungswerten ''z''
><math>\,</math>1 bis auf statistische Fluktuationen
allmählich verschwinden. Bemerkenswerterweise enthalten die
entsprechenden PLANCK-Kataloge <ref>P.A.R. Ade et al. (Planck
Collaboration),
[http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck
Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref> tatsächlich ganz überwiegend Beobachtungen bis etwa zu dieser Grenze.

Es ist jedenfalls nicht länger möglich, in der bloßen Existenz der CMB
Hintergrundstrahlung einen sicheren Beweis für eine Big-Bang Entstehung
des gesamten Universums zu sehen.

== Der alternative Sunyaev-Zel'dovich Effekt ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - Die CMB-Anteile
<math>\rho _Z^*</math>, die gemäß SUM von ''außerhalb'' der
Grenze <math>z = Z</math> kommen. Die durchgezogenen dünnen
roten Linien zeigen dies ''von oben nach unten'' für
<math>Z</math> = 0.1, 0.2, .. 1.0.]]

Der nach Rashid Sunyaev und Yakov Zel’dovich benannte Effekt beschreibt
eine in gewissen Frequenzbereichen leichte Abschwächung der
Hintergrundstrahlung durch Galaxienhaufen. Anders als im
''Konkordanzmodell'' sollte sich dieser Effekt gemäß vorläufiger
Erklärung im Rahmen von SUM mit zunehmender Entfernung abschwächen und
bei Rotverschiebungswerten größer als Eins allmählich verschwinden.
Bemerkenswerterweise enthält der entsprechende Katalog der
PLANCK-2013-Ergebnisse tatsächlich nur Beobachtungen bis etwa zu dieser
Grenze. Im Jahr 2015 wurde tatsäclich ein 'Sunyaev-Zel'dovich prediction cluster count mismatch' konstatiert.

Mit den Planck 2015 Daten und der Möglichkeit einer unvoreingenommenen
neuen Statistik des Sunyaev-Zel'dovich Effekts gibt es nun eine reelle
Chance, endgültig zu entscheiden, ob die CMB Hintergrundstrahlung einst
tatsächlich nach einem 'Big Bang' entstanden ist oder eben nicht: ob sie also stattdessen umgekahrt vom 'dunkler' Materie innerhalb eines
nicht-expandierenden Universums emittiert wird.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - Der realistische SZ-Effekt
zusammen mit einem Beispiel anderer CMB-Verzerrungen wie z.B.
zurück-verschiebender Inhomogenitäten.
-- '''''Obere Abb. (a)''''': Isotherme CMB-Fluktuationen der Ordnung
<math>y</math> ≈ 10^{-4} sind schwach rot gezeichnet,
wohingegen die dünnen gebogenen blauen und grauen Linien Änderungen des
lokalen SZ-Effekts zeigen.
-- '''''Untere Abb. (b)''''': Diese hoch-bedeutsame Abbildung
demonstriert ein resultierendes SZ-Signal als fettgedrucke rote Linie
(<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot
10^{-5}</math>), wobei die gemäß SUM resultierende ''isolierte''
Fequenz-Verschiebung durch solch eine zufällige
Hintergrund-Inhomogenität weitgehend aufgehoben wäre [kleinere
Intensitäten könnten als kleinere Werte der Clustermassen (in y)
interpretiert werden].]]

== Andere Beobachtungstatsachen und offene Fragen ==
Zusätzlich zu den im Rahmen von SUM besonders einfach beschreibbaren
kosmologischen Beobachtungstatsachen von universaler Rotverschiebung und den Supernova-Ia-Helligkeiten, die als zwei fundamentale Stützpfeiler
der [[wikipedia-de:Urknall|Urknall-Theorie]] gelten, scheinen auch weitere
Sachverhalte – bisher allerdings vor allem ansatzweise – alternativ
erklärbar.

* Nukleosynthese – In einem nach Voraussetzung stationären Universum ist der jeweilige Anteil aller materiellen Komponenten dadurch bestimmt, dass diese im Einklang mit den Gesetzen der Quantenmechanik in ''originären'' Prozessen wiederhergestellt werden, und zwar im gleichen Verhältnis, wie sie zuvor in Gravitationszentren extremer Stärke verschwunden sind. Das [[wikipedia-de:Urknall|Urknall]]-Modell benutzt an keiner Stelle, dass es außerhalb des dort ins Auge gefassten Bereichs extremer Temperaturen und Dichten nicht weitere solcher Ereignisse (''multi bangs'') geben könnte. Es kann auch nicht ausgeschlossen werden, dass die Freisetzung von Materie in Form von [[wikipedia-de:Jet (Astronomie)|Jets]] – mitsamt anschließender Bildung von [[wikipedia-de:Plasma|Plasma]]-Blasen – für eine ständige Wiederherstellung [[wikipedia-de:Primordiale Nukleosynthese|primordialer]] Kerne und ihrer Bestandteile sorgen.

* Quasar-Verteilung (und ältere Galaxienformen in großen Entfernungen) – Seit in den 1960er Jahren festgestellt wurde, dass der [[wikipedia-de:Quasar|Quasar]] [[wikipedia-de:3C 273|3C 273]] kein naher Stern ist, sondern mit einer
[[wikipedia-de:Rotverschiebung|Rotverschiebung]] von ''z'' = 0,158 im Bereich ferner Galaxien liegt, wurden in späteren Beobachtungen diese hellen sternartigen Gebilde in sehr viel größeren Entfernungen erkannt. Quasare wurden inzwischen bis zu einer Rotverschiebung von mindestens ''z'' = 7,1 entdeckt, woraus folgt, dass sich die nächsten von ihnen aus heutiger Sicht in kosmischer Nachbarschaft befinden. Selbst eine endgültige Beobachtung, dass sich solche
''[[wikipedia-de:Quasar|''Quasistellaren Objekte]]'' tatsächlich nur in überdurchschnittlichen Entfernungen befänden, wäre eine Selbstverständlichkeit, wenn die Evolution unseres 'lokalen' evolutionären Kosmos in einem ''Multi-Bang''-Ereignis – verträglich mit SUM – ihren Anfang genommen hätte; aus dem gleichen Grund könnten auch die meisten der sehr weit entfernten Galaxien tatsächlich jünger aussehen. Demgegenüber scheint die gemessene Häufigkeitsverteilung von Quasaren derzeit auf sehr großen Skalen ab ''z'' > 2-3 durch [[wikipedia-de:Selbstselektion|Selbstselektionseffekte]] wie dem so genannten ''[[wikipedia-de:Gunnar Malmquist|Malmquist-Bias]]'' zunächst reduziert und dann begrenzt zu sein, wobei alle Objekte unterhalb einer schwachen Helligkeitsgrenze unberücksichtigt bleiben.

* Grundsätzliche SUM-Unterschiede zu einer Urknall-Entstehung aus dem Nichts – Obwohl diverse als ''Säulen'' der [[wikipedia-de:Urknall|Urknall-Kosmologie]] bezeichnete fundamentale Beobachtungstatsachen numerisch glänzend bestätigt sind, bleiben doch wichtige Fragen. Ein ''[[wikipedia-de:Vakuumenergie|falsches Vakuum]]'' von ''[[wikipedia-de:Vakuumfluktuation|Quantenfluktuationen]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref>, wenn unser evolutionärer Kosmos daraus gemäß der [[wikipedia-de:Urknall|Urknall-Theorie]] entstanden wäre, könnte insgesamt nicht ohne Energiedichte gewesen sein, so dass ein solches ''[[wikipedia-de:Tohuwabohu|Tohu-va-bohu]]'' auch als universaler ''[[wikipedia-de:Urknall#chaotische Inflation|chaotischer Hintergrund]]'' der Beschreibung durch [[wikipedia-de:Albert Einstein|Einsteins]]
[[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] bedarf. Außer im Rahmen von SUM scheint eine Lösung nicht vorzuliegen. Hier aber tauchen solche und ähnliche Probleme der
''[[wikipedia-de:Lambda-CDM-Modell|Konkordanzkosmologie]]'' gar nicht auf, oder sie erscheinen in einem anderen Licht.

* Einschränkung des Entropiesatzes auf evolutionäre Prozesse – Bei gravitativen Neuentstehungsprozessen, möglicherweise in supermassereichen Objekten wie [[wikipedia-de:Aktiver Galaxienkern|aktiven Galaxienkernen (AGNs)]],
[[wikipedia-de:Hypernova|Hypernovae]] oder Quellen von [[wikipedia-de:Gammablitz|Gammablitzen]], sollte die [[wikipedia-de:Entropie|Entropie]] in lokalen Bereichen eines ewigen Universums zeitweilig abnehmen, damit sie insgesamt stationär bleiben kann. Dazu bedarf es einer Einschränkung des Gesetzes von der ständigen Zunahme der [[wikipedia-de:Entropie#Zweiter Hauptsatz|Entropie]] auf evolutionäre Prozesse, ohne dass dies einer von Lebewesen gemachten experimentellen Erfahrung jemals widersprechen könnte. Die Notwendigkeit einer vorübergehenden örtlich begrenzten Abnahme der Entropie ist unumgänglich für jedes stationäre Konzept überhaupt (ansonsten wäre ein lange diskutierter
''[[wikipedia-de:Wärmetod (Physik)|Wärmetod des Universums]]'' unvermeidlich). So unwahrscheinlich eine solche Einschränkung aber klingen mag,
so ist sie physikalisch doch weniger unwahrscheinlich als eine Entstehung des gesamten Universums aus dem ''[[wikipedia-de:Inflation (Kosmologie)#Entstehung aus dem Nichts?|Nichts]]''.

Zur Überwindung fundamentaler ''Fine-Tuning''-Probleme der
[[wikipedia-de:Urknall|Urknall-Theorie]], welche die ''Flachheit'' des Universums
oder die Nicht-Existenz ''magnetischer Monopole'' oder dessen
''Horizont'' betreffen, wurde eine Phase ''[[wikipedia-de:Inflation (Kosmologie)|kosmischer Inflation]]'' erdacht. Diese soll von einem
skalaren ''[[wikipedia-de:Inflation (Kosmologie)#Felddynamik| Inflatonfeld]]''
getrieben worden sein, das allerdings niemals experimentell beobachtet
worden ist. Auch die Tatsache der universalen
''[[wikipedia-de:Materie-Antimaterie-Asymmetrie|Materie-Antimaterie-Asymmetrie]]'' ist im Rahmen der gegenwärtig
vorherrschenden Kosmologie mit konkreter experimenteller Erfahrung nicht vereinbar. Ebenso wenig wäre gemäß der ursprünglichen
[[wikipedia-de:Urknall|Urknall-Theorie]] verständlich, dass es seit einer Entstehung
aus dem Nichts überhaupt gleichbleibende Naturgesetze gibt, und nicht
alles Geschehen bis heute nur vollkommen chaotisch abläuft. Irritierend
ist auch die Berufung auf ein ''imperfektes'' [[wikipedia-de:Kosmologisches Prinzip|Kosmologisches Prinzip]], das aus der ansonsten universalen Symmetrie nur die Zeit
willkürlich ausschließt. Das vielleicht größte aller
''Koinzidenz-Probleme'' besteht darin, dass die gewöhnlich als ''Alter
des Universums'' bezeichnete Zeitspanne ''t''0
ausgerechnet heutzutage näherungsweise mit dem Kehrwert der
konventionellen [[wikipedia-de:Hubble-Konstante|Hubble-Konstante]] 1/''H''0
übereinstimmen soll. Das ''[[wikipedia-de:Anthropisches Prinzip|anthropische Prinzip]]'' betrifft gemäß SUM nicht das stationäre Universum selbst,
sondern die möglichen evolutionären Kosmen darin. Durch die inzwischen
erfolgte Erweiterung des [[wikipedia-de:Urknall|Urknall]]-Konzepts – von ursprünglich einem
einzigen ''Big Bang''-Universum über zusätzliche
''[[wikipedia-de:Parallelwelt|Paralleluniversen]]'' bis hin zu einem nun wieder
allumfassenden ''[[wikipedia-de:Parallelwelt|Multiversum]]'' – scheint sich die
Kosmologie schließlich auf das SUM-Konzept mit seiner natürlichen
Unterscheidung des stationären Universums von evolutionären
''Multi-Bang''- bzw. lokalen ''Quasi-Bang''-Kosmen hinzuentwickeln. Es
ist im Zusammenhang mit vermeintlichem Alter und vermuteten Grenzen des
Universums bemerkenswert, dass Vorstellungen darüber immer wieder
erweitert wurden, seit [[wikipedia-de:Immanuel Kant|Immanuel Kant]] in schon damals beobachtbaren
Sternnebeln zum Teil ferne ''[[wikipedia-de:Milchstraße|Milchstraßen]]'' erkannte.

== Zur Vereinbarkeit von Relativitätstheorie und Quantenmechanik ==
In ''Geometrie und Erfahrung''<ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref> hat [[wikipedia-de:Albert Einstein|Albert Einstein]] sechs Jahre nach
Vollendung der [[wikipedia-de:Allgemeine Relativitätstheorie|allgemeinen Relativitätstheorie]] zwei mögliche Deutungen einander gegenübergestellt und dabei [[wikipedia-de:Henri Poincaré|Poincarés]] Auffassung der
[[wikipedia-de:Nichteuklidische Geometrie|nichteuklidischen Geometrie]]<ref>H.
Poincaré, [https://archive.org/details/wissenschaftundh00poin "''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L.
Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice
Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
grundsätzlich anerkannt ("''Sub specie aeterni hat Poincaré mit dieser
Auffassung nach meiner Meinung Recht''"). Demzufolge ist es möglich, die nichteuklidische Geometrie der allgemeinen Relativitätstheorie nicht
Raum und Zeit selbst, sondern gravitativ beeinflussten Maßstäben, Uhren
und allen anderen realen physikalischen Objekten zuzuschreiben und
ansonsten die [[wikipedia-de:Euklidische Geometrie|euklidische Geometrie]] zur
vollständigen Beschreibung des Naturgeschehens beizubehalten. Das
gelingt mit Hilfe einer von [[wikipedia-de:Nathan Rosen|Nathan Rosen]] formulierten ''bimetrischen Relativitätstheorie'' (bi-metric relativity)<ref>N. Rosen,
"''Flat-Space Metric in General Relativity Theory''", Ann. of Physics
22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>. Eine
solche Möglichkeit würde andererseits auch erklären, warum es bisher
trotz großer Anstrengungen ([[wikipedia-de:Stringtheorie|Stringtheorie]],
[[wikipedia-de:Schleifenquantengravitation|Schleifenquantengravitation]]) nicht überzeugend gelungen scheint, die ''[[wikipedia-de:Raumzeit|Raumzeit]]'' zu quantisieren und so die in herkömmlichem Sinne
verstandene [[wikipedia-de:Relativitätstheorie|Relativitätstheorie]] grundsätzlich mit der
[[wikipedia-de:Quantenmechanik|Quantenmechanik]] in einer [[wikipedia-de:allgemeine Relativitätstheorie#Quantenphysik|einheitlichen Theorie von Gravitation und Quantenmechanik]] zu vereinbaren.
Gemäß SUM-Ansatz aber scheint eine Vereinheitlichung prinzipiell möglich, um künftig gültige Aussagen zu
andernfalls bloßen mathematischen [[wikipedia-de:Singularität (Astronomie)|Singularitäten]] der allgemeinen Relativitätstheorie
überhaupt machen zu können, oder wenigstens Fehldeutungen zu verhindern. Dies betrifft neben der Theorie ''[[wikipedia-de:allgemeine Relativitätstheorie#Schwarze Löcher|schwarzer Löcher]]'' auch die
[[wikipedia-de:Singularitäten-Theorem|Singularitätstheoreme]] von [[wikipedia-de:Stephen Hawking|Hawking]] und [[wikipedia-de:Roger Penrose|Penrose]], bei denen in
Ermangelung einer konsistenten Theorie die tatsächliche Quantenstruktur
der Materie bisher außer acht bleiben musste.

== Numerische Hinweise auf die Existenz von 24 elementaren Spin-½ Torsionsteilchen ==

Obwohl mit dem Äquivalenzprinzip in seiner bisherigen Form unvereinbar,
gibt es einen klaren Hinweis auf die Materialisation eines
antisymmetrischen Windungstensors <math>T_{ikl}</math>. Das
Universum scheint demzufolge aus 24 Sorten von Spin-1/2 Partikeln
zusammengesetzt, nämlich aus 6 Arten von Leptonen plus 3 Farben mal 6
Sorten Quarks. Dies entspricht gerade den 24 Komponenten eines
Windungstensors, von denen 6 als 'zeitlich' plus 3*6 als 'räumlich' zu
bezeichnen sind:

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

Schon vor langer Zeit haben Landau & Lifschitz gezeigt, dass die
reale Existenz eines Windungstensors dem Einstein'schen
Äquivalenzprinzip widrsprechen müsste, welches der geometrischen
Interpretation seiner Gravitationsgleichungen zugrundeliegt.
Demgegenüber scheitert der Versuch aus Sicht von SUM, di Physik auf
Riemannsche Eigenschaften einer nicht-Euklidischen 'Raumzeit'
zurückzuführen. Damit scheitert letztlich auch die gesamte
Big-Bang-Kosmologie.

Im Hinblick auf ausgedehnte elementare Spin-1/2-Strukturen (die sich in
den meisten Situationen identfizierbar als ganze verhalten) werden auch
Heisenbergs Unchärferelationen verständlich, ganz im Unterschied zum
Verhalten ansonsten bisher unrealistischerweise vorausgesetzter
'Punkt-Teilchen' wie z.B. Elektronen oder Protonen. Diese sind keine
ausdehnungslosen 'Massen-Punkte' sondern natürlich aausgegdehnte
deformierbare Strukturen mit Teilchen-Parametern in Form konstanter
Integrale für u.a. Spin, Ladung, Ruhemasse. Insbesondere die
quantenmechanische Tatsaache, dass Teilchen im allgemeinen keinen
scharfen Impuls haben, ist angesichts relativer innerer Verschiebungen
ledigkich eine natürliche Feststellung.

Das Torsionskonzept ist unabhängig von der Frage, ob solche Teilchen als materielle Objekte im Vakuum existieren oder in Form von
Wirbelstrukture in einem kontinuierlich ausgedehnten Medium. Die Natur
kann beide Aspekte zeigen (wie bei Spiralnebeln in einem Hintergrund
dunkler Materie).
Die folgende Möglichkeit scheint ''evident'': 
– Elementarteilchen sind Wirbelstrukturen. 
– Aufgrund des Drehimpulserhaltungssatzes sind die winzig
ausgedehnten freien Wirbelstrukturen teilweise über
astronomische Zeiträume beständig. 
– Wirbelstrukturen unterliegen Entstehungs- und
Vergehungsprozessen. 
– In Übergangsphasen verlieren Wirbelstrukturen ihre
Identität. 
– Wirbelstrukturen lassen sich in einer Hinsicht
näherungsweise beschreiben als Teilchen. 
– Wirbelstrukturen lassen sich in anderer Hinsicht
näherungsweise beschreiben als Wellen. 
– In Wirbelstrukturen sind detaillierte Geschwindigkeiten ihrer
Bestandteile und die statistischen Geschwindigkeiten der
jeweiligen Schwerpunktbewegung gleichzeitig realisiert,
woraus sich ganz natürlich Unschärfebeziehungen ergeben. 
Demnach scheinen die Elementarteilchen, aus denen das gesamte Universum
aufgebaut ist, wesentlich verschieden von jenen ewigen festen 'Atomen'
der bahnbrechenden antiken Philosophen Leukipp und Demokrit. Nachdem
klar ist, dass Torsionspartikel nur um den Preis unvermeidlicher
Unschärfen als audehnungslose Punktteilchen behandelt werden dürfen,
muss eine vollständige relativistische Mechanik zukünftig eine
konsistente Formulierung der Quantenmechanik enthalten. Eine geeignete
Basis dafür bietet Rosens 'bi-metrische' Formulierung der
Relativitätstheorie, nachdem sie nun in das (ausgezeichnete) universale
Bezugssystem eingebunden ist.

== Historisches, SUM-Vorläufer, verschiedene verwandte Ansätze ==

Es ist ganz unmöglich, Kosmologie zu betreiben ohne geeignete
Prinzipien, welche - neben der unverzichtberen Verträglichkeit mit
eindeutigen Beobachtungstatsachen - die Kriterien von Einfachheit,
Angemessenheit und Klarheit zu erfüllen haben. Ohne solche Kriterien
wäre gemäß Allgemeiner Relativitätstheorie aufgrund legitimer
Koordinatentransformaionen heute nicht einmal mehr die kopernikanische
Entscheidung zwischen einem heliozentrischen und einem geozentrischen
Planetensystem eindeutig möglich.

Albert Einstein ist bei seiner Begründung der relativistischen
Kosmologie<ref>A. Einstein,
"''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''",
Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref> von der
Voraussetzung eines ewigen Universums ausgegangen. Dieser Versuch ist
daran gescheitert, dass er eine rein ''statische'' Lösung gesucht hat,
deren Linienelement – im Unterschied zu dem Linienelement [[wikipedia-de:Alexander Alexandrowitsch Friedmann|Friedmanns]] wie auch zu demjenigen des
stationären Ansatzes SUM – eine Zeitkoordinate in den entsprechenden
Gravitationspotentialen ''gik'' nicht enthält.
Dies galt auch für die ursprüngliche Form des [[wikipedia-de:De-Sitter-Modell|De-Sitter-Modell]]s, die sich aber durch bloße Koordinatentransformation in das Linienelement
der späteren Steady-State-Theorie überführen ließ.

* Steady-State-Theorie: Unter dem Namen [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]], die eine beständige Expansion beschreiben sollte, wurde im Jahr 1948 ein später (in unterschiedlichen Versionen) an Beobachtungstatsachen gescheitertes Modell des Universums präsentiert, das nach Auffassung seiner Autoren aufgrund ständiger Schöpfung aus dem Nichts als von gleichbleibender Materiedichte erfüllt anzusehen war. Erst in jüngster Zeit wurde bekannt, dass bereits Einstein das Konzept dieser Theorie im wesentlichen vorweggenommen und verworfen hat. Im Unterschied zu SUM wird hier eine ständige Schöpfung aus dem Nichts beschrieben, wobei sich ein von [[wikipedia-de:Fred Hoyle|Fred Hoyle]] eingeführtes ''C''-Feld als Vorläufer des Skalarfeldes des heutigen Inflationsmodells verstehen lässt. Die Rotverschiebungswerte jeweiliger Galaxien ergeben sich in der [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] nicht statistisch konstant, sondern würden entsprechend den zitierten Titeln jener Arbeiten (mit ausdrücklichem Bezug auf ein ''expandierendes Universum'') ständig zunehmen.

* Coasting Cosmology: Ein Modell mit allgemeinerer als der oben angegebenen FLRW-Form des SUM-Linienelements – jedoch mit [[wikipedia-de:Skalenfaktor|Skalenfaktor]] ''HT'' – wurde seinerzeit unter dem Aspekt einer ''gleitenden'' Expansion des Universums diskutiert<ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, bevor 2011 (und später) ein
eng damit verwandtes Konzept noch einmal im Kontext der [[wikipedia-de:Urknall|Urknall-Kosmologie]] behandelt wurde<ref>F. Melia & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct universe''"], MNRAS 419, 2579, 2012</ref>. Beide unterscheiden sich grundsätzlich von SUM (die fundamentale Konsequenz gleichbleibender Rotverschiebungswerte von Quellen in gleichbleibenden universalen Entfernungen wurde nicht erwähnt).

* Chaotic Inflation: Der Physiker [[wikipedia-de:Andrei Dmitrijewitsch Linde|Andrei Linde]] hat das Konzept einer [[wikipedia-de:Urknall#chaotische Inflation|chaotischen Inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> entwickelt und dabei die theoretische Fixierung auf einen einzigen Urknall aus dem Nichts effektiv aufgehoben. Andererseits wird dort von ''Parallel''-Universen gesprochen, wovon jedes mit eigener Inflation und gegebenenfalls eigenen Naturgesetzen entstanden sei. Zu den Grundvoraussetzungen von SUM – viele kosmische Bereiche in einem einzigen Universum mit überall gleichen Naturgesetzen – steht das in klarem Widerspruch. In diesem Zusammenhang (obwohl in völlig anderem mathematischen Kontext) ist auch der Begriff 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> erstmalig aufgetaucht.

Hinsichtlich eines ewig im Wandel befindlichen Universums hat es
offenbar schon immer entsprechende Vorstellungen gegeben. Diese scheinen verwandt zum [[wikipedia-de:Samsara|Kreislauf von Werden und Vergehen]] in östlichen Religionen. Nach Auffassung [[wikipedia-de:Epikur|Epikur]]s existieren in einem unendlich
großen Raum eine unendliche Anzahl von Welten. Darüber wurde von Lukrez
in ''[[wikipedia-de:De rerum natura|Über die Natur der Dinge]]'' berichtet. Gemäß
[[wikipedia-de:Rhazes|Rhazes]] sollen – im Sinne zeitloser Naturgesetze – eine ewige Materie aus Atomen, eine absolute und ewige (im Unterschied zur 'geschaffenen'
Welt aber relative) Zeit sowie ein absoluter und ewiger (im Unterschied
zur 'geschaffenen' Welt aber relativer) Raum unveränderlich vorgegeben
sein. Ähnliche Konzepte von Raum und Zeit finden sich später bei Newton. [[wikipedia-de:Nikolaus von Kues|Nikolaus von Kues]] hat sich eine [[wikipedia-de:Parallelwelt|Vielheit von Welten]] in einem einzigen unbegrenzten Universum gedacht. Die im Sinne
moderner Naturwissenschaft neubelebte Vorstellung eines ewigen
unendlichen [[wikipedia-de:Universum|Universum]]s aber existiert spätestens seit
[[wikipedia-de:Thomas Digges|Thomas Digges]]. Sein Zeitgenosse [[wikipedia-de:Giordano Bruno|Giordano Bruno]] verteidigte die Idee
''vieler Welten'', wie insbesondere aus seiner Schrift ''Über die
Unendlichkeit, das Universum und die Welten'' von 1584 hervorgeht (der
Wortwahl dieses Titels entspricht auch die SUM-Unterscheidung von
''Universum'' und ''Kosmen''). Er hatte dabei die Vorstellung, dass das
[[wikipedia-de:Giordano Bruno#Unendlichkeit des Weltalls|ewige unendliche Universum]] ''von demselben göttlichen Puls durchwirkt'' sei. Sein Denken wurde
von den genannten Vorgängern beeinflusst. Im Rahmen von SUM wurde nun
gezeigt, dass sich entsprechende Konzepte nicht nur mit Einsteins
Gleichungen vereinbaren lassen, sondern sich aus diesen zu ergeben
scheinen. Einerseits wird zwar dieses neue Modell von der
Mainstream-Kosmologie bisher kaum wahrgenommen, doch andererseits
scheint das aktuelle ''Konkordanzmodell'' mit seiner teilweise
hochspekulativen (durch keine experimentelle Erfahrung konkret
begründeten, aber dort unverzichtbaren)
''[[wikipedia-de:Inflation (Kosmologie)|Inflationsphase]]'' bei nicht wenigen Menschen auf
zunehmende Skepsis zu stoßen.

Die Idee von SUM - als der einzigen diskutablen Alternative der
originalen Gravitationsleichungen Einsteins ohne kosmologische Konstante - ist, dass keine univeralen Horizonte die physsikalische Realität
beschränken dürfen. Außerhalb ihrer lokalen Anwendbarkeit erweisen sich
alle Konzepte der Speziellen Relativitätsteorie im Rahmen der
konventionell verstandenen Allgemeinen Relativitätsteorie als
überinterpretiert. Deshalb braucht SUM eine wissenschaftliche Diskussion statt endloser Scheingefechte gegen längst überholte historische
Versuche wie der alten SST. Kosmologische Theorien sind nicht dazu da,
die Natur belehren zu wollen, sondern von ihr zu lernen und sie in
Ehrfurcht und gebotener Bescheidenheit zu beschreiben.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia-de:Kategorie: Kosmologie (Physik)- DEUTSCH|Kategorie: Kosmologie (Physik)- DEUTSCH]] --
[[wikipedia-de:Benutzer:Nimos15|Nimos15]] ([[wikipedia-de:Benutzer Diskussion:Nimos15|Diskussion]]) 12:15, 10 Mar 2018 (CET)

Stationary Universe Model (SUM)

2026-02-21T13:16:06Z

Admin:

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values ('Hubble Trouble') for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref> <ref>A.G. Riess et al., [http://arxiv.org/abs/1801.01120 "New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant"], [http://dx.doi.org/10.3847/1538-4357/aaadb7 doi:10.3847/1538-4357/aaadb7], [http://arxiv.org/abs/1801.01120 "arxiv:1801.01120"]</ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data <ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM_model|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM [[wikipedia:distance_modulus|distance modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:absolute_magnitude|magnitude]] is represented by ''m'' and the [[wikipedia:brightness|absolute brightness]] of [[wikipedia:type_Ia_Supernova|Supernovae type Ia]] [[wikipedia:cosmic_distance_ladder|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Einstein-de_Sitter_universe|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements <ref>P. Ostermann, [http://independent-research.org/assets/nobel-prize-physics-2011.pdf "The well-earned Nobel Prize for the wrong reason"]</ref>.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:homogeneity_and_heterogeneity|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:gravitational_lense|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:critical_density|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:expansion_of_the_universe|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting those authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Planck spectrum of redshifted microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:dark_matter|'dark matter']]''. This concept may solve two fundamental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:black_body|Planck spectrum]] out of [[wikipedia:redshift|redshifted]] radiation without the hypothesis of a 'big bang' <ref>P. Ostermann, [http://independent-research.org/assets/sum_os14.pdf "Model of a Stationary Background Universe Behind Our Cosmos"], 2013 (chapter 2.8)</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "A microwave background of redshifted radiation within the stationary universe, (chapter 5 of "Problems ... " s. above)"]</ref>.

At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:thermal_radiation|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:acoustic oscillations|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:anisotropy|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:black_body|Planck spectrum]] seems [[wikipedia:falsifiable|falsifiable]] with help of the [[wikipedia:Sunyaev%E2%80%93Zel%27dovich_effect|Sunyaev–Zel'dovich effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM <ref>P. Ostermann, [http://independent-research.org/assets/dm1_peter_ostermann_(ulti).pdf "Homogeneously distributed dark matter of second kind as an alternative to 'dark energy"], Talk MG14 in Rome, also explaining the concept of 24 spin-1/2 torsion particles</ref> <ref>P. Ostermann, [http://independent-research.org/assets/cm2_3_peter_ostermann_(ulti).pdf "The PLANCK 2015 model prediction mismatch of Sunyaev-Zeldovich cluster counts and a universal microwave background composed of redshifted radiation from 'dark' matter"], Talk MG14 in Rome </ref> that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:primordial|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a [[wikipedia:redshift|redshift]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar object|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:effects of self selection|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:big_bang|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:false_vacuum|false vacuum]]'' of ''[[wikipedia:quantum fluctuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:big_bang|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:chaotic_inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:graviational_equations|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active_galaxy_nuclei|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:gamma-ray|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Second_law_of_thermodynamics|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:thermodynamics|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:big_bang|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:inflation_(cosmology)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:inflation_(cosmology|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter_asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:big_bang|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble's law|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:anthropic_principle|anthropic principle]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems further to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:general relativity|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:non-euclidean geometry|non-euclidean geometry]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia:euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in [[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]] no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:unified_theory|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:singularity|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:black_holes|black holes]]'' this also concerns the [[wikipedia:Penrose%E2%80%93Hawking_singularity_theorems|singularity theorems]] of [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Sir Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor_(cosmology)|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Linde|Andrei Linde]] has developed the concept of [[wikipedia:eternal_inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been correspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epicurus|Epicurus]] there exists an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:plurality_of_worlds|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. This insight goes back to a seminal analysis ""Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"" of Einstein's ideas<ref>P. Ostermann, [http://arxiv.org/abs/gr-qc/0208056 "Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"]</ref>. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T13:14:12Z

Admin:

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values ('Hubble Trouble') for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref> <ref>A.G. Riess et al., [http://arxiv.org/abs/1801.01120 "New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant"], [http://dx.doi.org/10.3847/1538-4357/aaadb7 doi:10.3847/1538-4357/aaadb7], [http://arxiv.org/abs/1801.01120 "arxiv:1801.01120"]</ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data <ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM_model|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM [[wikipedia:distance_modulus|distance modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:absolute_magnitude|magnitude]] is represented by ''m'' and the [[wikipedia:brightness|absolute brightness]] of [[wikipedia:type_Ia_Supernova|Supernovae type Ia]] [[wikipedia:cosmic_distance_ladder|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Einstein-de_Sitter_universe|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements <ref>P. Ostermann, [http://independent-research.org/assets/nobel-prize-physics-2011.pdf "The well-earned Nobel Prize for the wrong reason"]</ref>.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:homogeneity_and_heterogeneity|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:gravitational_lense|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:critical_density|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:expansion_of_the_universe|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting those authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Planck spectrum of redshifted microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:dark_matter|'dark matter']]''. This concept may solve two fundamental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:black_body|Planck spectrum]] out of [[wikipedia:redshift|redshifted]] radiation without the hypothesis of a 'big bang' <ref>P. Ostermann, [http://independent-research.org/assets/sum_os14.pdf "Model of a Stationary Background Universe Behind Our Cosmos"], 2013 (chapter 2.8)</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "A microwave background of redshifted radiation within the stationary universe, (chapter 5 of "Problems ... " s. above)"]</ref>.

At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:thermal_radiation|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:acoustic oscillations|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:anisotropy|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:black_body|Planck spectrum]] seems [[wikipedia:falsifiable|falsifiable]] with help of the [[wikipedia:Sunyaev%E2%80%93Zel%27dovich_effect|Sunyaev–Zel'dovich effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM <ref>P. Ostermann, [http://independent-research.org/assets/dm1_peter_ostermann_(ulti).pdf "Homogeneously distributed dark matter of second kind as an alternative to 'dark energy"], Talk MG14 in Rome, also explaining the concept of 24 spin-1/2 torsion particles</ref> <ref>P. Ostermann, [http://independent-research.org/assets/cm2_3_peter_ostermann_(ulti).pdf "The PLANCK 2015 model prediction mismatch of Sunyaev-Zeldovich cluster counts and a universal microwave background composed of redshifted radiation from 'dark' matter"], Talk MG14 in Rome </ref> that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:primordial|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a [[wikipedia:redshift|redshift]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar object|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:effects of self selection|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:big_bang|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:false_vacuum|false vacuum]]'' of ''[[wikipedia:quantum fluctuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:big_bang|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:chaotic_inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:graviational_equations|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active_galaxy_nuclei|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:gamma-ray|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Second_law_of_thermodynamics|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:thermodynamics|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:big_bang|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:inflation_(cosmology)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:inflation_(cosmology|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter_asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:big_bang|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble's law|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:anthropic_principle|anthropic principle]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems further to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:general relativity|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:non-euclidean geometry|non-euclidean geometry]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia:euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in [[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]] no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:unified_theory|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:singularity|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:black_holes|black holes]]'' this also concerns the [[wikipedia:Penrose%E2%80%93Hawking_singularity_theorems|singularity theorems]] of [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Sir Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor_(cosmology)|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Linde|Andrei Linde]] has developed the concept of [[wikipedia:eternal_inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been correspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epicurus|Epicurus]] there exists an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:plurality_of_worlds|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. This insight goes back to a seminal analysis ""Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"" of Einstein's ideas<ref>P. Ostermann, [http://arxiv.org/abs/gr-qc/0208056 "Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"]</ref>. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T13:13:55Z

Admin:

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values ('Hubble Trouble') for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref> <ref>A.G. Riess et al., [http://arxiv.org/abs/1801.01120 "New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant"], [http://dx.doi.org/10.3847/1538-4357/aaadb7 doi:10.3847/1538-4357/aaadb7], [http://arxiv.org/abs/1801.01120 "arxiv:1801.01120"]</ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data <ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM_model|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM [[wikipedia:distance_modulus|distance modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:absolute_magnitude|magnitude]] is represented by ''m'' and the [[wikipedia:brightness|absolute brightness]] of [[wikipedia:type_Ia_Supernova|Supernovae type Ia]] [[wikipedia:cosmic_distance_ladder|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Einstein-de_Sitter_universe|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements <ref>P. Ostermann, [http://independent-research.org/assets/nobel-prize-physics-2011.pdf "The well-earned Nobel Prize for the wrong reason"]</ref>.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:homogeneity_and_heterogeneity|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:gravitational_lense|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:critical_density|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:expansion_of_the_universe|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting those authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Planck spectrum of redshifted microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:dark_matter|'dark matter']]''. This concept may solve two fundamental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:black_body|Planck spectrum]] out of [[wikipedia:redshift|redshifted]] radiation without the hypothesis of a 'big bang' <ref>P. Ostermann, [http://independent-research.org/assets/sum_os14.pdf "Model of a Stationary Background Universe Behind Our Cosmos"], 2013 (chapter 2.8)</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "A microwave background of redshifted radiation within the stationary universe, (chapter 5 of "Problems ... " s. above)"]</ref>.

At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:thermal_radiation|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:acoustic oscillations|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:anisotropy|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:black_body|Planck spectrum]] seems [[wikipedia:falsifiable|falsifiable]] with help of the [[wikipedia:Sunyaev%E2%80%93Zel%27dovich_effect|Sunyaev–Zel'dovich effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM <ref>P. Ostermann, [http://independent-research.org/assets/dm1_peter_ostermann_(ulti).pdf "Homogeneously distributed dark matter of second kind as an alternative to 'dark energy"], Talk MG14 in Rome, also explaining the concept of 24 spin-1/2 torsion particles</ref> <ref>P. Ostermann, [http://independent-research.org/assets/cm2_3_peter_ostermann_(ulti).pdf "The PLANCK 2015 model prediction mismatch of Sunyaev-Zeldovich cluster counts and a universal microwave background composed of redshifted radiation from 'dark' matter"], Talk MG14 in Rome </ref> that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:primordial|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a [[wikipedia:redshift|redshift]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar object|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:effects of self selection|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:big_bang|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:false_vacuum|false vacuum]]'' of ''[[wikipedia:quantum fluctuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:big_bang|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:chaotic_inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:graviational_equations|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active_galaxy_nuclei|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:gamma-ray|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Second_law_of_thermodynamics|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:thermodynamics|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:big_bang|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:inflation_(cosmology)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:inflation_(cosmology|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter_asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:big_bang|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble's law|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:anthropic_principle|anthropic principle]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems further to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:general relativity|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:non-euclidean geometry|non-euclidean geometry]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia:euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in [[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]] no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:unified_theory|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:singularity|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:black_holes|black holes]]'' this also concerns the [[wikipedia:Penrose%E2%80%93Hawking_singularity_theorems|singularity theorems]] of [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Sir Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor_(cosmology)|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Linde|Andrei Linde]] has developed the concept of [[wikipedia:eternal_inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been correspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epicurus|Epicurus]] there exists an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:plurality_of_worlds|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. This insight goes back to a seminal analysis ""Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"" of Einstein's ideas<ref>P. Ostermann, [http://arxiv.org/abs/gr-qc/0208056 "Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"]</ref>. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM) - Deutsch

2026-02-21T13:13:02Z

Admin: Stand Juni 2018

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

Das Modell '''SUM''' ('''Stationary Universe Model''') wurde seit 2001 von dem Physiker ''Peter Ostermann'' aus der Voraussetzung eines
ewigen, unendlichen Universums als offenes Projekt (''work in progress'') entwickelt und auf Basis der
originalen [[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]]
[[wikipedia-de:Albert Einstein|Albert Einstein]]s <ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die
Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25.
November 1915, 844-847 – (reprint Doc. 25, CPAE Vol.
6)</ref><ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 –
(reprint Doc. 30 CPAE Vol. 6)</ref> ohne [[wikipedia-de:Kosmologische Konstante|Kosmologische Konstante]] als vernünftige Alternative<ref>P. Ostermann,
"''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und
die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054,
2002/04</ref> zum numerisch außerordentlich erfolgreichen
[[wikipedia-de:Urknall#Expansion des Universums|Urknallmodell]] phyikalisch
formuliert. Es wurde beim 12. [[wikipedia-de:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]<ref>P.
Ostermann,
"''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230
Relativistic Deduction of a Stationary Tohu-va-Bohu Background
Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.),
Proc. MG12, W.Sci., 1408-1410, 2012;
[http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref><ref>P. Ostermann,
"''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219
Indication from the Supernovae Ia Data of a Stationary Background
Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.),
Proc. MG12, W.Sci., 1373-1375, 2012;
[http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref> in Paris vorgestellt (MG12 2009, zuvor
bei der DPG-Frühjahrstagung<ref>P. Ostermann,
"''[http://independent-research.org/assets/07a.pdf Das relativistische
Modell eines stationären Hintergrunduniversums und die
Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref> 2007
Heidelberg, erste pre-prints bei arXiv.org). Gegenüber dem aufgrund
exzellenter scheinbarer Bestätigungen seit langem vorherrschenden
[[wikipedia-de:Kosmologie|Standard-Modell]] (''Konkordanzmodell'') in Form der
[[wikipedia-de:Inflation (Kosmologie)|inflationären]]
[[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Kosmologie]] stellt SUM auf Basis eines
neuen Linienelements ein Konzept dar, das im Gegensatz zu der trotz
übereinstimmender Motivation überholten [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] mit
aktuellen kosmologischen Beobachtungstatsachen vereinbar scheint. Trotz
verblüffender Erfolge hat das Modell hinsichtlich diverser Details nicht innerhalb weniger Jahre den hochentwickelten Stand der nahezu
ausgereiften Konkordanzkosmologie erreichen können, sondern befindet
sich noch in einer Anfangsphase; es versteht sich als Ermutigung im
Sinne der ''Aufklärung'': "sapere aude!" (wage zu denken).

<div style="color:red">
Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allowing for the solution of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.
</div>

Das neue kosmologische Modell SUM eines stationären
Hintergrund-Universums beinhaltet keine [[wikipedia-de:Expansion des Universums|Expansion des Raums]]. Es geht aus von der physikalischen
Tatsache, dass aus Nichts nichts entsteht. Das [[wikipedia-de:Weltall|Weltall]] wird als eine insgesamt beständige Gegebenheit betrachtet und im Sinne des
''stationären'' – nicht aber statischen – ''Universums'' von unserem
''[[wikipedia-de:Urknall|evolutionären Kosmos]]'' unterschieden. Alter und Ausdehnung des Universum sind demzufolge unendlich, nicht aber unser Kosmos als
Teil davon.

Was sonst als 'Alter des Universums' bezeichnet wird, stellt sich aus
Sicht von SUM heraus als das Höchstalter makroskopischer Strukturen wie
dem von Sternen, Galaxien, (Super-)Cluster gegebenenfalls bis hin zu dem Höchstalter ganzer Kosmen. Scheinbar gegenteilige Beobachtungen
ältester Galaxien könnnen von einem einzigen gemeinsamen Ursprung nicht
überzeugen. Dies steht in Analogie zu der alltäglichen Erfahrung, dass
das Höchstalter individueller Menschen nicht etwa das Alter der gesamten Population beweist. Im Unterschied zur natürlichen Suche nach der
vitalen Vergangenheit unseres evolutionären Kosmos macht es keinen Sinnnnach einer historischen Entwicklung des ewigen Universums zu fragen.

Trotz gemeinsamer Voraussetzung des ''[[wikipedia-de:Kosmologisches Prinzip|perfekten kosmologischen Prinzips]]'' unterscheidet sich das Model SUM mit statistisch konstanten Werten der [[wikipedia-de:Rotverschiebung|Rotverschiebung]] kosmischer
Strahlungsquellen fundamental von der [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] eines
expandierenden Universums<ref>H. Bondi & T. Gold,
[http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State
Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref><ref>F. Hoyle,
[http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New
Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical
Society, vol. 108, 372-382, 1948</ref>. Die mathematisch exakt
abgeleiteten gleichbleibenden SUM-Rotverschiebungswerte entsprechen den
nach Voraussetzung statistisch gleichbleibenden [[wikipedia-de:Euklidische Geometrie|euklidischen]] Entfernungen in ''universalen Koordinaten'',
die aus historischen Gründen auch als ''[[wikipedia-de:Entfernungsmaß#Mitbewegte Entfernung|mitbewegt]]'' bezeichnet werden (''comoving coordinates'').
Nach einer zunächst rein mathematischen Ableitung der ''stationären''
[[wikipedia-de:Hintergrundstrahlung|Hintergrundstrahlung]] mit [[wikipedia-de:Plancksches Strahlungsgesetz|Planck-Spektrum]] (ohne Zurückführung auf einen
[[wikipedia-de:Urknall|Urknall]]) wurde eine SUM-Vorgängerversion<ref>P. Ostermann,
"''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a
Heuristic Approach from a Stationary Universe]''",
arXiv:astro-ph/0312655v6, 2013</ref> weiterentwickelt und zu
''Model of a Stationary Background Universe Behind Our Cosmos'' (2013)
ausgebaut. - Sämtliche zugrunde liegenden Arbeiten stehen auf
[http://independent-research.org "independent-research.org"] zum
Download bereit.

== Das stationäre Linienelement ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – Die
Zuordnungen (<math>\Omega_\mathrm{M}</math>, <math>
w_\mathrm{M} </math>,
<math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0,
0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') =
\mathrm{e}^{Ht'}</math> [obere graue durchgezogene Linie], eine
erste Alternative zu <math>a_\mathrm{CCM}(t')</math> mit
größerem Wert <math>\Omega_\mathrm{\Lambda}</math>) [blaue
gestrichelte Linie], das heutige Concordance Model
<math>a_\mathrm{CCM}(t')</math> [blaue durchgezogene Linie], das stationäre ultra-large scale Universum
<math>a_\mathrm{SUM}(t') = HT'</math> =
<math>1+Ht'</math> [rote gerade Linie], eine zweite Variante zu <math>a_\mathrm{CCM}(t')</math> mit kleinerem Wert
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken
line], das Einstein-de-Sitter Modell <math>a_\mathrm{EdS}(t') =
</math> <math>(1 +
\mathrm{3/2}Ht')^\mathrm{2/3}</math> [untere graue durchgezögene
Linie, favorisiert vor dem SNe-Ia Durchbruch]. Im Kontrast zu anderen
vergleichbaren Werten scheinen die CCM best-fit Parameter
<math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid
line) festgelegt durch die Bedingung, dass ihre Linie den
SUM-Skalenfaktor (rot) an seinen 'Grenzen', d.h. bei HT' = -1 und bei
Ht' ≈ 0 heute treffen sollte. ]]

Im Unterschied zu ''statisch'' besagt ''stationär'', dass ein Zustand
insgesamt gleich bleibt, obwohl sich einzelne Bestandteile ständig
verändern können. Dem Konzept SUM liegt, anders als bei der
''[[wikipedia-de:Induktion (Philosophie)|induktiven]]'' Entwicklung der
[[wikipedia-de:Urknall|Urknall-Kosmologie]], ein ''[[wikipedia-de:Deduktion|deduktiver]]'' Ansatz
zugrunde. Dabei genügen zwei [[wikipedia-de:Postulat|Postulate]], um das hier
zugrundeliegende stationäre [[wikipedia-de:Metrischer Tensor#Linienelement|Linienelement]] abzuleiten:

* Postulat I – In Bezug auf hinreichend große Skalen ist das Universum stationär, homogen und isotrop;
* Postulat II – Abgesehen von lokalen Abweichungen ist die universale Lichtgeschwindigkeit ''c''* = ''c'' .

Aus diesen beiden außerordentlich einfachen Postulaten ergibt sich das
SUM-Linienelement d''σ''*SUM eines räumlich
''flachen'', nicht leeren Universums eindeutig zu:
<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math> .
Hier steht ''H'' für eine wahre ''Hubble-Konstante'' (die im Unterschied zum zeitabhängigen ''konventionellen'' [[wikipedia-de:Hubble-Konstante#Definition|Hubble-Parameter]] ''H''0 der
[[wikipedia-de:Urknall|Urknall-Kosmologie]] als ''signifikant'' bezeichnet wird); die Abkürzung d''σ''*SRT steht für das Linienelement der [[wikipedia-de:Spezielle Relativitätstheorie|speziellen Relativitätstheorie]],
wobei das zusätzliche Symbol
'<math>\,</math>*<math>\,</math>' bei jedem
Auftreten auf die Besonderheit hinweist , dass sich die entsprechenden
Größen auf ''universale Koordinaten'' beziehen (neben den
'[[wikipedia-de:Entfernungsmaß#Mitbewegte Entfernung|mitbewegten Koordinaten]]'
''l''<math>\,</math>* auch die 'konforme Zeit'
''t''<math>\,</math>*). Gemäß SUM stimmen die universalen
Koordinaten immer wieder vorübergehend überein mit den ''[[wikipedia-de:Umgebung (Mathematik)|lokalen]]'' [[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlängen]] und
[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeiten]] der speziellen
Relativitätstheorie. Aus dem ausgeschriebenen Quadrat des Linienelements ist die Konstanz der universalen [[wikipedia-de:Lichtgeschwindigkeit|Lichtgeschwindigkeit]] mit c* ≡
d''l''<math>\,</math>*/d''t'' * = c (für
d''σ''*SUM = 0) sofort ersichtlich. Das
SUM-Linienelement hat weitere bemerkenswerte Eigenschaften.

== Rotverschiebung und signifikante Hubble-Konstante ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - Die SUM
Voraussage des im Rahmen der Lambda-CDM 'big-bang' Kosmologie völlig
unverständlichen Hubble-Kontrasts. -
Zwei verschieden Werte für die Hubble 'Kostante'
<math>H_{\mathrm{local}}</math> =
<math>H_{\mathrm{CCM}}</math> und
<math>H_{\mathrm{universal}}</math> =
<math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:'''''
Die blaue durchgezogene Linie repräsentiert die realen Werte
<math>z_{\mathrm{observed}}</math> der SNe-Ia-Messungen, die rote unterbrochene SUM Linie vernachlässigt mögliche 'peculiar flows' oder lokale Inhomogenitäten. Die maximale Abweichung <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c innerhalb
<math>z</math> < 0.027 entspricht einem maximalen
Kontrast <math>H_{\mathrm{local}}</math> /
<math>H_{\mathrm{universal}}</math> - 1} von ungefähr 9% an
diesem Punkt wo <math>H_{\mathrm{universal}}</math> ≈ 67
km/s/Mpc.

'''''-- Bottom panel (b)}:'''''
Innerhalb <math>r^* < 110</math> Mpc entspricht die blaus Linie <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc,
wohingegen der mittlere Wert in der Übergangszone (bis
<math>z</math> ≈ 0.13) ungefähr
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc beträgt. Die
Differenz führt von
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈
4.7% bis zu
<math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% und entspricht annähernd gerade dem Bereich des lokalen
Hubble-Kontrasts von 6.5% ± 1.8%., wie er von Jha, Riess & Kirshner
berichtet wird}.
]]

Es ist einfach falsch zu behaupten, dass die kosmische Rotverschiebung
eine Expansion des Universums beweist.
Die ''universale Rotverschiebung'' des Lichts entfernter
[[wikipedia-de:Galaxie|Galaxien]] und anderer Strukturen wird im Rahmen von SUM nicht als [[wikipedia-de:Doppler-Effekt|Doppler-Effekt]], sondern im Sinne einer erweiterten
Einsteinschen [[wikipedia-de:Rotverschiebung#Gravitative Rot- und Blauverschiebung|Gravitationsrotverschiebung]] verstanden, woraus sich
wie auch beim Experiment von [[wikipedia-de:Pound-Rebka-Experiment|Pound und Rebka]]
keine Fluchtbewegung zwischen Quelle und Empfänger ergibt (bereits
[[wikipedia-de:Edwin Hubble|Edwin Hubble]]<ref>E.P. Hubble,
[http://www.pnas.org/content/15/3/168.full "''A relation between
distance and radial velocity among extra-galactic nebulae''"], Proc. N.
Acad. Sci. 15, 168-173, 1929</ref> hatte eine solche Möglichkeit
in Betracht gezogen). Der Unterschied zur gewöhnlichen
[[wikipedia-de:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitativen Rot- und Blauverschiebung]] liegt hier darin, dass es sich im Falle von
SUM um ein ''zeitabhängiges'' Potential handelt, das sich aufgrund des
Vorzeichens immer als ''Rotverschiebung'' auswirkt. Aus der allgemeinen
Definition des [[wikipedia-de:Rotverschiebung|Rotverschiebungsparameters]]
''z'' =
''λ''<math>\,</math>beobachtet /
''λ''<math>\,</math>ausgestrahlt – 1
ergeben sich bei SUM mit
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
solche Werte, die mit der ''signifikanten'' Hubble-Konstante ''H''
unabhängig sind von der Zeit. Diese Werte gelten für Galaxien und alle
kosmologischen Strukturen, die sich in Bezug auf universale Koordinaten
(''x''*, ''y''*, ''z''*) nach Voraussetzung statistisch in Ruhe befinden (die Unabhängigkeit von der Zeit gilt auch für alle anderen Größen, die sich als Funktion der Rotverschiebung ''z'' schreiben lassen).
Insbesondere bedeutet deren Zeitunabhängigkeit, dass zusätzlich zu den
lokalen [[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlängen]] der SRT
nun auch den universalen Entfernungen
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
wegen gleichbleibender Rotverschiebungen entsprechender Objekte eine
reale, physikalisch messbare Bedeutung zukommt. Im Gegensatz zur
[[wikipedia-de:Urknall|Urknall-Theorie]] stellt die universale Entfernung ''l''* im
Rahmen von SUM also eine selbständige – obwohl indirekte – Messgröße
dar.

== Universale Zeit ''t''<math>\,</math>* und die Grenzen von Eigenlänge und Eigenzeit ==
Wegen der exponentiellen Form des Zeitskalars e''Ht'' * hängen relative zeitliche Änderungen e''Ht'' */ e''Ht''o* =
e''H''(''t'' *– ''t''o*) allein ab von
''Differenzen'' Δ<math>\,</math>''t'' * = ''t'' * – ''t''0*. Der gleiche Sachverhalt erlaubt es auch, für beliebige zusammenhängende Ereignisse (dies betrifft insbesondere auch [[wikipedia-de:Spontane Emission|Emission]] und spätere [[wikipedia-de:Absorption (Physik)|Absorption]] von Photonen) den universalen zeitlichen
Anfangspunkt jeweils ''t''0* = 0 zu setzen. Im
Unterschied zur jeweiligen lokalen ''Quasi-Eigenzeit'' ''t'' ' = ''T'' ' – ''T''H (mit der [[wikipedia-de:Hubble-Zeit|Hubble-Zeit]] ''T''H = 1/''H'') ist kein spezieller Punkt der universalen Zeitskala ''t''<math>\,</math>* ausgezeichnet.
Die universale Zeit hat weder Anfang noch Ende. Gemäß dem Linienelement
der in begrenzten Bereichen überall und immer wieder lokal gültig
bleibenden speziellen Relativitätstheorie
(d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) sind
die Intervalle von ''[[wikipedia-de:Beobachter (Physik)#Relativitätstheorie|Eigenlänge]]'' und
''[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeit]]'' stets miteinander gemeinsam
definiert. Wie daraus mathematisch folgt, können die sich in Bezug auf
das SUM-Linienelement ergebenden Näherungen
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
nur innerhalb lokal begrenzter Bereiche
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
des unendlichen euklidischen Raums (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2) jeweils
vorübergehend Gültigkeit beanspruchen (''R''H =
''c''/''H'' ist der [[wikipedia-de:Beobachtbares Universum#Hubble-Radius|Hubble-Radius]]). Gleiches gilt für alle
SRT-Konzepte überhaupt. Bei uneingeschränkter Gleichheit in den obigen
Näherungen aber würde das SUM-Linienelement in dasjenige der SRT übergehen, und der resultierende Einstein-Tensor würde unzulässigerweise verschwinden (was einer universalen Energiedichte Null und damit einem
leeren Universum entspräche). Diese Zusammenhänge ergeben sich aus einer zweifachen [[wikipedia-de:Koordinatentransformation|Koordinatentransformation]] ''t'' * =
ln<math>\,</math>(''HT''
')<math>\,</math>/<math>\,</math>''H'' und ''l'' * = ''l''
'<math>\,</math>/<math>\,</math>(''HT'' '),
wobei ''T'' ' näherungsweise einer ''Eigenzeit'' entspricht, die nach
obiger Ungleichung jeweils örtlich eingeschränkt ist.

== Die FLRW-Form des SUM-Linienelements ==
Wird nur die universale Zeit ''t'' * gemäß der ersten der beiden oben
angegebenen Formeln transformiert, so folgt das stationäre Linienelement in einer
[[wikipedia-de:Friedmann-Lemaître-Robertson-Walker-Metrik|Friedmann-Lemaître-Robertson-Walker-Form (FLRW-Form)]], und zwar mit dem einfachsten aller in Frage kommenden
[[wikipedia-de:Skalenfaktor|Skalenfaktor]]en
''a''<math>\,</math>SUM = ''HT'' ' zu

:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math> ,
ohne dass sich damit an den physikalischen Tatsachen etwas ändert. Es
lässt sich z.B. leicht verifizieren, dass der zeitunabhängige
SUM-Zusammenhang zwischen der Rotverschiebung ''z'' und der universalen
Entfernung ''l''<math>\,</math>* auch gemäß dieser FLRW-Form bestehen bleibt. Es ist im Hinblick auf die gesamte SUM-Kosmologie von
entscheidender Bedeutung, dass sich die auftretende
'Anfangs'-Singularität der örtlich eingeschränkten ''Quasi-Eigenzeit T'' ' = 0 nur auf lokale Bereiche bezieht und keineswegs ein Alter des
gesamten Universums darstellt. Stattdessen bedeutet sie, wie oben
gezeigt, eine jeweils auf ''l''<math>\,</math>* <
''R''H eingeschränkte maximale Lebensdauer
räumlich begrenzter evolutionärer Strukturen (in Bezug auf die
universale Zeitkoordinate entspricht ''T'' ' = 0 dabei ''t'' * = –oo.

== Energiedichte und negativer Gravitationsdruck ==
Die bei SUM offenbar der ''universalen Energiedichte'' entsprechende
Komponente ''G''00 des [[wikipedia-de:Tensor#Ko- und Kontravarianz|''kovarianten'']]
[[wikipedia-de:Friedmann-Gleichung#Herleitung|Einstein-Tensor]]s ist zeitlich
konstant. Demgegenüber scheint die [[wikipedia-de:Krummlinige Koordinaten#Tensoren zweiter Stufe|gemischt ko- kontravariante]] Komponente
''G''00, die bei Anwendung der [[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] auf lokale [[wikipedia-de:Ideale Flüssigkeit|perfekte Flüssigkeiten]] der
[[wikipedia-de:Phänomenologie|''phänomenologisch'']]''en'' Energiedichte entspräche,
abhängig von der ''universalen Zeit t''<math>\,</math>*.
Dass aber eine solche Abhängigkeit über beliebig große universale
Zeiträume im Unterschied zu lokal begrenzten
[[wikipedia-de:Zeitdilatation#Eigenzeit|Eigenzeiten]] ''t'' unrealistisch wäre, folgt wieder aus der Tatsache, dass kein spezieller Anfangspunkt der
Zeitskala ''t''<math>\,</math>* existiert.

Aus dem SUM-Linienelement ergibt sich zu jedem willkürlich wählbaren
universalen zeitlichen Anfangspunkt ''t''0* = 0
ein negativer Gravitationsdruck von –1/3 der ''[[wikipedia-de:kritische Dichte|kritischen Dichte]]'', dessen Existenz hier sofort einleuchtet.
Im Unterschied zu gewöhnlichen Teilchen in einem Kasten (die sich ohne
dessen Wände aufgrund ihres positiven Drucks sofort
[[wikipedia-de:Diffusion|zerstreuen]]) würden Galaxien innerhalb eines begrenzten
Bereichs des stationären Universums ohne negativen Gravitationsdruck (verursacht vom Gravitationspotential der Materie und Energie außerhalb) zusammenklumpen, was in Bezug auf hinreichend große Skalen nach
Voraussetzung nicht geschehen kann.

== SUM Vorhersage zweier verschiedener Werte für die lokale und die universelle Hubble-Konstante ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Links (a)-(e)''''': Der Vergleich der SUM magnitude-redshift Voraussage (für ''κ'' = 0) mit den original SNe-Ia Daten und der CCM-Voraussage zeigt eine unmittelbare SUM-Übereinstimmung auf universalen Skalen z > 0.1, auf denen das Universum am ehesten zu Recht als homogen und isotrop betrachtet werden darf. Die rote SUM-Linie fällt beinahe vollständig mit der blauen CCM-Linie zusammen (trotz - oder: wegen - der gegenüber der lokalen um 9% höheren ''universalen'' Hubble-Konstante).
 -- '''''Intermediate panels (b),(d)''''': Mit
dem in Abb. W2 gezeigten lokalen Hubble-Kontrast existiert nun eine
volle SUM-Übereinstimmung nicht nuur mit den SNe-Ia Daten des 'High-z
Supernova Search Teams' (Riess et al.) sondern auch mit Kowalskis 2008
Union 'world' Zusammenstellung des 'Supernova Cosmology Projects'
(Perlmutter et al.).
Offensichtlich genügen die Korrekturen von maximal <math>\mathrm
\delta z </math> ≈ 0.002 im Bereich <math>z {\mathrm{observed}}</math> < 0.027 für eine befriedigende
Übereinstimmung von SUM mit den Daten
im Falle des lokalen Hubble-Kontrasts
analog W2 auch im Bereich jeweils kleiner Rotverschiebungswerte.
 -- '''''Lower panels (c),(e)''''': In diesen CCM-Abbildungen sind die
blau-gestrichelten geraden Linien nach der Methode der kleinsten
quadratischen Abweichungen bestimmt und sollten sich im Idealfall als
kongruent zur jeweiligen z-Achse erweisen.
: ]]

In beiden Teilen der Abbilddung W2 repräsentieren die blauen
duchgezogenen Linien die realen SNe-Ia Messungen, wohingegen die
gebrochenen roten Linien (jeweils darunter) für SUM stehen. Eine
maxiimale Abweichhung <math> \mathrm \delta z </math> ≈
0.002 entspricht einem maximalen Huble-Kontrast von ≈+9%. Mit
<math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc würde das
<math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc innerhalb
<math> \mathrm{r^{\ast}}</math> < 110 Mpc
<math>(\mathrm \delta z </math> < 0.027) bedeuten,
während sich der Mittelwert in der Übergangszone gerade auf ungefähr
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc beläuft.

Nun wurde kürzlich von Riess als zweitem der zitierten Autoren ein
"lokaler Wert" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc
berichtet
<ref>A.G. Riess et al.,
[http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A
2.4% Determination of the Local Value of the Hubble Constant''"], ApJ
826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]],
[http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
mit einer Toleranz von nur 2.4% (sowie 71.9 km/s/Mpc ±3.8%, was
annähernd übereinstimmt mit 72.8 km/s/Mpc ±3.3% in Bonvin e al.
<ref>V. Bonvin et al.,
[http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New
COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong
lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790
"arXiv:1607.01790]" </ref>.
Nahe bei Freedman's Wert von 72 km/s/Mpc
<ref>W. L. Freedman et al.,
[http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results
from the Hubble Space Telescope Key Project to Measure the Hubble
Constant''"], ApJ, 553:47È72, 2001</ref>
aber in klarem Kontrast zu den von der
Lambda-CDM Kosmologie gemäß der neuen Planck 'high-redshift'-Messungen
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical
depth''"], A&A 596, A107 (2016)</ref>
vorausgesagten 67 km/s/Mpc – oder auch anähernd zu den 68 km/s/Mpc von
Cheng Cheng \& Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119
"''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801
</ref>
bedeutet das ausgerechnet wieder einen Hubble-Kontrast von etwa +9%,
welcher Wert beinahe perfekt mit der original SUM-Vorhersage von 2007
übereinstimmt.

Anscheinend setzen die Autoren Riess et al. des neuen Reports zu Unrecht den gekümmmten Verlauf ihres eigenen unzutreffenden Lambda-CDM
Hubble-Diagramms voraus (und zwar ohne jede ausdrückliche
Rechtfertigunng). Deshalb können sie natürlch auch keinen Unterschied
zwischen der lokalen und der universellen Hubble-Konstante finden,
obwohl es im urspünglichen Artikel von Jha, Riess & Kirshner
überzeugend heißt: ''"... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology."'' <ref>S. Jha, A.G. Riess, &
R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/
"''Improved Distances to Type Ia Supernovae with Multicolor Light Curve
Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere
Literturangaben darin)</ref>

Nun beweist aber das Auftreten zweier verschiener Werte der
Hubble-Konstante das konsistente SUM-Konzept geradezu. Dies zeigt auch,
dass es ebenso andere unerwartete Zusammenhänge geben könnte, die noch
zu entdecken bzw. im Rahmen von SUM zu erklären sind. So scheint es
nicht unmöglchh, auf dieser Bais mit Hilfe von 'high
precision'-Messungen scheinbarer Helligkeiten die Energie-Massen-Dichte
unserer anisotropen kosmischen Nachbarschaft genauer zu ermitteln.

== Vergleich mit den Supernova-Ia-Daten ==
Die zitierte Feststellung von Riess et al. 2011, dass ihr gemessener
Wert von H0 ebenfalls hochgradig inkonsistent ist mit den einfachsten
Modellen inhomogener Materie, die zur Erklärung der scheinbaren
Beschleunigung des Universums ohne 'dunkle Energie' aufgerufen sind
("measured H0 is also highly inconsistent with the simplest
inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"), beruht auf einem populären
Trugschluss indem dabei der fiktive "Big-Bang" als sicheres Szenario von Anfang an einfach vorausgesetzt wird. Tatsächlich aber läßt sich diese
Behauptung duch einen simplen Plot ihrer eigenen SNeIa 'gold'-Daten im
universalen Rotverschiebungsbereich z > 0.1 leicht widerlegen (diese
Widerlegung braucht nicht einmal irgendwelches eigenes
astrophysikalisches Fachwissen, da ihre öffentlich verfügbaren und mit
dem Nobelpreis ausgezeichneten zugrundeliegenden Daten zu Recht als
unanfechtber gelten).

Zur Erklärung der Supernova-Ia-Daten<ref>A.G. Riess et al. (High-z Supernova Search Team), [http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble
Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref><ref>M. Kowalski et al. (The Supernova Cosmology
Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/
"''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> auf
hinreichend großen universalen Skalen benötigt das Modell SUM keine
'dunkle Energie' und unterscheidet sich auch damit vom
[[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Modell]] als dem Standardmodell der gegenwärtigen
[[wikipedia-de:Kosmologie|Kosmologie]]. Abweichungen im Bereich ''z'' < 0.1 werden hier auf
einen lokalen Hubble-Kontrast zurückgeführt, wie er in entsprechender
Größenordnung
tatsächlich beobachtet wurde. Der universale SUM-[[wikipedia-de:Absolute Helligkeit|Entfernungsmodul]] ergibt sich nach bewährter Vorgehensweise
aus dem stationären Linienelement zu
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math> ,
wobei die [[wikipedia-de:Scheinbare Helligkeit|Magnitude]] ''m'' ein Maß für die
[[wikipedia-de:Scheinbare Helligkeit|scheinbare Helligkeit]], und ''M'' einen
geeignet zu wählenden Wert für die [[wikipedia-de:Absolute Helligkeit|absolute Helligkeit]] beispielsweise
von [[wikipedia-de:Supernova vom Typ Ia|Supernovae Typ Ia]] (SNe-Ia) als [[wikipedia-de:Standardkerze|''Standardkerzen'']] darstellt. Das
MG12-Dokument ''Indication from the Supernovae Ia Data of a Stationary
Background Universe''<ref>P. Ostermann,
[http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (sinnvollerweise im pdf-Ganzseitenmodus
durchzublättern)</ref> zeigt die unmittelbare Übereinstimmung des
SUM-Entfernungsmoduls mit den Supernova-Daten für ''universale''
Rotverschiebungswerte ''z'' > 0.1 (erst oberhalb solcher,
größenordnungsmäßig der [[wikipedia-de:Sloan Great Wall|Sloan Great Wall]] entsprechender Skalen kann
das Universum als homogen und isotrop betrachtet werden). Darin geht aus einer Reihe systematisch aufeinanderfolgender Abbildungen auch hervor,
warum zur Vermittlung zwischen den Voraussagen des erwarteten
[[wikipedia-de:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter-Modells]] und denjenigen der alten [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] das Konzept einer die kosmologische Konstante repräsentierenden 'dunklen Energie' notwendig
schien. Wird aber an den originalen
[[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] ohne
[[wikipedia-de:kosmologische Konstante|kosmologische Konstante]] festgehalten, so hätten die SNe-Ia-Messungen das SUM-Linienelement offensichtlich bestätigt. Im Rahmen der
entsprechenden Berechnungen ergibt sich aufgrund universaler
[[wikipedia-de:Rotverschiebung|Rotverschiebung]] und [[wikipedia-de:Zeitdilatation|Zeitdilatation]] selbst bei unendlich vielen
Sternen ein realistischer endlicher Wert für die Helligkeit des
Nachthimmels, so dass das [[wikipedia-de:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olberssche Paradoxon]] auch ohne die Annahme eines Urknalls
oder einer Expansion des Raums hier gelöst ist.

== Alternative zum materiellen Beitrag der 'dunklen Energie' ==
Zusätzlich zu indirekt beobachteten oder durch
[[wikipedia-de:Gravitationslinseneffekt|Gravitationslinseneffekte]] gemessenen
[[wikipedia-de:Inhomogenität|Inhomogenitäten]] sollte es im Rahmen von SUM einen
annähernd homogen verteilten, optisch ebenfalls transparenten Beitrag
einer ''dunklen'' Materie geben, der sich ''nicht'' durch solche
[[wikipedia-de:Gravitationslinseneffekt|Gravitationslinseneffekte]] nachweisen lässt. Dieser homogene Anteil, der im [[wikipedia-de:Lambda-CDM-Modell|Lambda-CDM-Modell]] einer
''[[wikipedia-de:Dunkle Energie#Beobachtung|dunklen Energie]]'' zugeschrieben wird, könnte hier
die Lücke schließen zwischen der insgesamt beobachteten Materie und der
[[wikipedia-de:Kritische Dichte|kritischen Dichte]], die für ein ''flaches'' Modell
ohne räumliche Krümmung notwendig ist. Gleichzeitig findet eine
[[wikipedia-de:Expansion des Universums|Expansion des Raums]] gemäß SUM nicht statt,
so dass auch in dieser Beziehung wieder keine zusätzliche Energie für
eine Beschleunigung erforderlich ist.

Es ist erwiesenermaßen eine falsche Feststellung in Riess et al. 2011 zu lesen ''"The measured <math>H_0</math> is also highly
inconsistent with the simplest inhomogeneous matter models invoked to
explain the apparent acceleration of the universe without dark energy"'' <ref>A.G. Riess et al.,
[http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3%
Solution: Determination of the Hubble Constant with the Hubble Space
Telescope and Wide Field Camera 3''"],
ApJ 730, 1-18+1, 2011</ref> (s. Fig. W3 instead).

Zusätzlich sei angemerkt, dass ... It may be remarked, that if dark matter was built in huge parts of
thermalized neutrinos, then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying these hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed to come from z > 1000). A preliminary
assessment on base of relation (82) would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, will make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Mikrowellenhintergrundstrahlung und eine 'dunkle Materie' ==

[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - Die
fettgedruckte durchgezogene schwarze Linie steht für das gesamte
CMB-Spetrum so wiie es im Falle <math>\kappa</math> = 2
tatsächlich beobachtet wird. Die fettgedruckte rote Linie zeigt am
Beispiel einer lokalen Kugel vom Radius <math>\Delta
r^*</math> = 100 Mpc die Emission der hDM-Strahlung wie sie sich
hier ergibt. Zusätzlich zeigen die dünnen durchgezogenen roten Linien die jeweiligen Anteile von innerhalb ''z'' = ''Z'' ''von unten nach oben'' mit ''Z'' = 0.1, 0.2, .. 1.0 in diesem Fall.
]]

Im Rahmen von SUM wird die [[wikipedia-de:Hintergrundstrahlung|Hintergrundstrahlung]] (CMB) zum Teil als
[[wikipedia-de:Wärmestrahlung|Wärmestrahlung]] der ''[[wikipedia-de:Dunkle Materie|'dunklen Materie']]''
gedeutet. Dieses Konzept könnte zwei fundamentale Probleme zugleich
lösen: (a) es gibt keine makroskopische Materieverteilung ohne
Temperatur und Wärmestrahlung; und (b) eine stationäre
Hintergrundstrahlung muss innerhalb des Universums entstanden sein. In
einer zunächst rein mathematischen Ableitung ist es gelungen, aus
[[wikipedia-de:Rotverschiebung|rotverschobenen]] Strahlungsanteilen ein perfektes
[[wikipedia-de:Plancksches Strahlungsgesetz|Planck-Spektrum]] ohne [[wikipedia-de:Urknall|Urknall]]
abzuleiten. Bei einer statistisch mittleren universalen Temperatur
scheinen die [[wikipedia-de:Inhomogenität|Inhomogenitäten]] dieser kalten
''[[wikipedia-de:Wärmestrahlung|Wärmestrahlung]]'' die offensichtlich vorhandenen
[[wikipedia-de:Baryonische akustische Oszillation|akustischen Oszillationen]] der
gesamten Materie widerzuspiegeln, die sich über astronomische Zeiträume
auch hier durch das Wechselspiel von [[wikipedia-de:Gravitation|Gravitation]] und
[[wikipedia-de:Strahlungsdruck|Strahlungsdruck]] ausgebildet hätten. Die Chance einer alternativen
Erklärung der CMB-[[wikipedia-de:Anisotropie|Anisotropien]] im Rahmen von SUM springt beim Vergleich verschiedener Abbildungen, beispielsweise Figure 14-e
von ''N. A. Sharp''<ref>N.A. Sharp,
[http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The
whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN
0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref> mit Figure
7(b) von ''C. L. Bennett''<ref>C.L. Bennett et al.,
[http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
oder mit Figure 5 von ''R. Piffaretti''<ref>R. Piffaretti et al.,
[http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray
detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>
nahezu ins Auge. Im Gegensatz zum Konzept eines ewigen unendlichen
Universums selbst, scheint die vorläufige Erklärung des
[[wikipedia-de:Planck-Spektrum|Planck-Spektrum]]s im Rahmen von SUM mit Hilfe des
[[wikipedia-de:Sunjajew-Seldowitsch-Effekt|Sunjajew-Seldowitsch-Effekt]]s [[wikipedia-de:Falsifikationismus|falsifizierbar]].
Dieser Effekt<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang,
[http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The
Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison
between the X-Ray Predicted and WMAP Observed Cosmic Microwave
Background Temperature Decrement"''], ApJ 648, 176-199,
2006</ref><ref>L.E. Bleem et al.,
[http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the
Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''],
ApJS, 216, 27, 2015</ref> sollte sich mit zunehmender Entfernung
abschwächen und ab Rotverschiebungswerten ''z''
><math>\,</math>1 bis auf statistische Fluktuationen
allmählich verschwinden. Bemerkenswerterweise enthalten die
entsprechenden PLANCK-Kataloge <ref>P.A.R. Ade et al. (Planck
Collaboration),
[http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster
counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080,
article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck
Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015
results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''",
article PDF 2015]</ref> tatsächlich ganz überwiegend Beobachtungen bis etwa zu dieser Grenze.

Es ist jedenfalls nicht länger möglich, in der bloßen Existenz der CMB
Hintergrundstrahlung einen sicheren Beweis für eine Big-Bang Entstehung
des gesamten Universums zu sehen.

== Der alternative Sunyaev-Zel'dovich Effekt ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - Die CMB-Anteile
<math>\rho _Z^*</math>, die gemäß SUM von ''außerhalb'' der
Grenze <math>z = Z</math> kommen. Die durchgezogenen dünnen
roten Linien zeigen dies ''von oben nach unten'' für
<math>Z</math> = 0.1, 0.2, .. 1.0.]]

Der nach Rashid Sunyaev und Yakov Zel’dovich benannte Effekt beschreibt
eine in gewissen Frequenzbereichen leichte Abschwächung der
Hintergrundstrahlung durch Galaxienhaufen. Anders als im
''Konkordanzmodell'' sollte sich dieser Effekt gemäß vorläufiger
Erklärung im Rahmen von SUM mit zunehmender Entfernung abschwächen und
bei Rotverschiebungswerten größer als Eins allmählich verschwinden.
Bemerkenswerterweise enthält der entsprechende Katalog der
PLANCK-2013-Ergebnisse tatsächlich nur Beobachtungen bis etwa zu dieser
Grenze. Im Jahr 2015 wurde tatsäclich ein 'Sunyaev-Zel'dovich prediction cluster count mismatch' konstatiert.

Mit den Planck 2015 Daten und der Möglichkeit einer unvoreingenommenen
neuen Statistik des Sunyaev-Zel'dovich Effekts gibt es nun eine reelle
Chance, endgültig zu entscheiden, ob die CMB Hintergrundstrahlung einst
tatsächlich nach einem 'Big Bang' entstanden ist oder eben nicht: ob sie also stattdessen umgekahrt vom 'dunkler' Materie innerhalb eines
nicht-expandierenden Universums emittiert wird.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - Der realistische SZ-Effekt
zusammen mit einem Beispiel anderer CMB-Verzerrungen wie z.B.
zurück-verschiebender Inhomogenitäten.
-- '''''Obere Abb. (a)''''': Isotherme CMB-Fluktuationen der Ordnung
<math>y</math> ≈ 10^{-4} sind schwach rot gezeichnet,
wohingegen die dünnen gebogenen blauen und grauen Linien Änderungen des
lokalen SZ-Effekts zeigen.
-- '''''Untere Abb. (b)''''': Diese hoch-bedeutsame Abbildung
demonstriert ein resultierendes SZ-Signal als fettgedrucke rote Linie
(<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot
10^{-5}</math>), wobei die gemäß SUM resultierende ''isolierte''
Fequenz-Verschiebung durch solch eine zufällige
Hintergrund-Inhomogenität weitgehend aufgehoben wäre [kleinere
Intensitäten könnten als kleinere Werte der Clustermassen (in y)
interpretiert werden].]]

== Andere Beobachtungstatsachen und offene Fragen ==
Zusätzlich zu den im Rahmen von SUM besonders einfach beschreibbaren
kosmologischen Beobachtungstatsachen von universaler Rotverschiebung und den Supernova-Ia-Helligkeiten, die als zwei fundamentale Stützpfeiler
der [[wikipedia-de:Urknall|Urknall-Theorie]] gelten, scheinen auch weitere
Sachverhalte – bisher allerdings vor allem ansatzweise – alternativ
erklärbar.

* Nukleosynthese – In einem nach Voraussetzung stationären Universum ist der jeweilige Anteil aller materiellen Komponenten dadurch bestimmt, dass diese im Einklang mit den Gesetzen der Quantenmechanik in ''originären'' Prozessen wiederhergestellt werden, und zwar im gleichen Verhältnis, wie sie zuvor in Gravitationszentren extremer Stärke verschwunden sind. Das [[wikipedia-de:Urknall|Urknall]]-Modell benutzt an keiner Stelle, dass es außerhalb des dort ins Auge gefassten Bereichs extremer Temperaturen und Dichten nicht weitere solcher Ereignisse (''multi bangs'') geben könnte. Es kann auch nicht ausgeschlossen werden, dass die Freisetzung von Materie in Form von [[wikipedia-de:Jet (Astronomie)|Jets]] – mitsamt anschließender Bildung von [[wikipedia-de:Plasma|Plasma]]-Blasen – für eine ständige Wiederherstellung [[wikipedia-de:Primordiale Nukleosynthese|primordialer]] Kerne und ihrer Bestandteile sorgen.

* Quasar-Verteilung (und ältere Galaxienformen in großen Entfernungen) – Seit in den 1960er Jahren festgestellt wurde, dass der [[wikipedia-de:Quasar|Quasar]] [[wikipedia-de:3C 273|3C 273]] kein naher Stern ist, sondern mit einer
[[wikipedia-de:Rotverschiebung|Rotverschiebung]] von ''z'' = 0,158 im Bereich ferner Galaxien liegt, wurden in späteren Beobachtungen diese hellen sternartigen Gebilde in sehr viel größeren Entfernungen erkannt. Quasare wurden inzwischen bis zu einer Rotverschiebung von mindestens ''z'' = 7,1 entdeckt, woraus folgt, dass sich die nächsten von ihnen aus heutiger Sicht in kosmischer Nachbarschaft befinden. Selbst eine endgültige Beobachtung, dass sich solche
''[[wikipedia-de:Quasar|''Quasistellaren Objekte]]'' tatsächlich nur in überdurchschnittlichen Entfernungen befänden, wäre eine Selbstverständlichkeit, wenn die Evolution unseres 'lokalen' evolutionären Kosmos in einem ''Multi-Bang''-Ereignis – verträglich mit SUM – ihren Anfang genommen hätte; aus dem gleichen Grund könnten auch die meisten der sehr weit entfernten Galaxien tatsächlich jünger aussehen. Demgegenüber scheint die gemessene Häufigkeitsverteilung von Quasaren derzeit auf sehr großen Skalen ab ''z'' > 2-3 durch [[wikipedia-de:Selbstselektion|Selbstselektionseffekte]] wie dem so genannten ''[[wikipedia-de:Gunnar Malmquist|Malmquist-Bias]]'' zunächst reduziert und dann begrenzt zu sein, wobei alle Objekte unterhalb einer schwachen Helligkeitsgrenze unberücksichtigt bleiben.

* Grundsätzliche SUM-Unterschiede zu einer Urknall-Entstehung aus dem Nichts – Obwohl diverse als ''Säulen'' der [[wikipedia-de:Urknall|Urknall-Kosmologie]] bezeichnete fundamentale Beobachtungstatsachen numerisch glänzend bestätigt sind, bleiben doch wichtige Fragen. Ein ''[[wikipedia-de:Vakuumenergie|falsches Vakuum]]'' von ''[[wikipedia-de:Vakuumfluktuation|Quantenfluktuationen]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref>, wenn unser evolutionärer Kosmos daraus gemäß der [[wikipedia-de:Urknall|Urknall-Theorie]] entstanden wäre, könnte insgesamt nicht ohne Energiedichte gewesen sein, so dass ein solches ''[[wikipedia-de:Tohuwabohu|Tohu-va-bohu]]'' auch als universaler ''[[wikipedia-de:Urknall#chaotische Inflation|chaotischer Hintergrund]]'' der Beschreibung durch [[wikipedia-de:Albert Einstein|Einsteins]]
[[wikipedia-de:Einsteinsche Feldgleichungen|Gravitationsgleichungen]] bedarf. Außer im Rahmen von SUM scheint eine Lösung nicht vorzuliegen. Hier aber tauchen solche und ähnliche Probleme der
''[[wikipedia-de:Lambda-CDM-Modell|Konkordanzkosmologie]]'' gar nicht auf, oder sie erscheinen in einem anderen Licht.

* Einschränkung des Entropiesatzes auf evolutionäre Prozesse – Bei gravitativen Neuentstehungsprozessen, möglicherweise in supermassereichen Objekten wie [[wikipedia-de:Aktiver Galaxienkern|aktiven Galaxienkernen (AGNs)]],
[[wikipedia-de:Hypernova|Hypernovae]] oder Quellen von [[wikipedia-de:Gammablitz|Gammablitzen]], sollte die [[wikipedia-de:Entropie|Entropie]] in lokalen Bereichen eines ewigen Universums zeitweilig abnehmen, damit sie insgesamt stationär bleiben kann. Dazu bedarf es einer Einschränkung des Gesetzes von der ständigen Zunahme der [[wikipedia-de:Entropie#Zweiter Hauptsatz|Entropie]] auf evolutionäre Prozesse, ohne dass dies einer von Lebewesen gemachten experimentellen Erfahrung jemals widersprechen könnte. Die Notwendigkeit einer vorübergehenden örtlich begrenzten Abnahme der Entropie ist unumgänglich für jedes stationäre Konzept überhaupt (ansonsten wäre ein lange diskutierter
''[[wikipedia-de:Wärmetod (Physik)|Wärmetod des Universums]]'' unvermeidlich). So unwahrscheinlich eine solche Einschränkung aber klingen mag,
so ist sie physikalisch doch weniger unwahrscheinlich als eine Entstehung des gesamten Universums aus dem ''[[wikipedia-de:Inflation (Kosmologie)#Entstehung aus dem Nichts?|Nichts]]''.

Zur Überwindung fundamentaler ''Fine-Tuning''-Probleme der
[[wikipedia-de:Urknall|Urknall-Theorie]], welche die ''Flachheit'' des Universums
oder die Nicht-Existenz ''magnetischer Monopole'' oder dessen
''Horizont'' betreffen, wurde eine Phase ''[[wikipedia-de:Inflation (Kosmologie)|kosmischer Inflation]]'' erdacht. Diese soll von einem
skalaren ''[[wikipedia-de:Inflation (Kosmologie)#Felddynamik| Inflatonfeld]]''
getrieben worden sein, das allerdings niemals experimentell beobachtet
worden ist. Auch die Tatsache der universalen
''[[wikipedia-de:Materie-Antimaterie-Asymmetrie|Materie-Antimaterie-Asymmetrie]]'' ist im Rahmen der gegenwärtig
vorherrschenden Kosmologie mit konkreter experimenteller Erfahrung nicht vereinbar. Ebenso wenig wäre gemäß der ursprünglichen
[[wikipedia-de:Urknall|Urknall-Theorie]] verständlich, dass es seit einer Entstehung
aus dem Nichts überhaupt gleichbleibende Naturgesetze gibt, und nicht
alles Geschehen bis heute nur vollkommen chaotisch abläuft. Irritierend
ist auch die Berufung auf ein ''imperfektes'' [[wikipedia-de:Kosmologisches Prinzip|Kosmologisches Prinzip]], das aus der ansonsten universalen Symmetrie nur die Zeit
willkürlich ausschließt. Das vielleicht größte aller
''Koinzidenz-Probleme'' besteht darin, dass die gewöhnlich als ''Alter
des Universums'' bezeichnete Zeitspanne ''t''0
ausgerechnet heutzutage näherungsweise mit dem Kehrwert der
konventionellen [[wikipedia-de:Hubble-Konstante|Hubble-Konstante]] 1/''H''0
übereinstimmen soll. Das ''[[wikipedia-de:Anthropisches Prinzip|anthropische Prinzip]]'' betrifft gemäß SUM nicht das stationäre Universum selbst,
sondern die möglichen evolutionären Kosmen darin. Durch die inzwischen
erfolgte Erweiterung des [[wikipedia-de:Urknall|Urknall]]-Konzepts – von ursprünglich einem
einzigen ''Big Bang''-Universum über zusätzliche
''[[wikipedia-de:Parallelwelt|Paralleluniversen]]'' bis hin zu einem nun wieder
allumfassenden ''[[wikipedia-de:Parallelwelt|Multiversum]]'' – scheint sich die
Kosmologie schließlich auf das SUM-Konzept mit seiner natürlichen
Unterscheidung des stationären Universums von evolutionären
''Multi-Bang''- bzw. lokalen ''Quasi-Bang''-Kosmen hinzuentwickeln. Es
ist im Zusammenhang mit vermeintlichem Alter und vermuteten Grenzen des
Universums bemerkenswert, dass Vorstellungen darüber immer wieder
erweitert wurden, seit [[wikipedia-de:Immanuel Kant|Immanuel Kant]] in schon damals beobachtbaren
Sternnebeln zum Teil ferne ''[[wikipedia-de:Milchstraße|Milchstraßen]]'' erkannte.

== Zur Vereinbarkeit von Relativitätstheorie und Quantenmechanik ==
In ''Geometrie und Erfahrung''<ref>A. Einstein,
[http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer,
Berlin 1921</ref> hat [[wikipedia-de:Albert Einstein|Albert Einstein]] sechs Jahre nach
Vollendung der [[wikipedia-de:Allgemeine Relativitätstheorie|allgemeinen
Relativitätstheorie]] zwei mögliche Deutungen einander gegenübergestellt und dabei [[wikipedia-de:Henri Poincaré|Poincarés]] Auffassung der
[[wikipedia-de:Nichteuklidische Geometrie|nichteuklidischen Geometrie]]<ref>H.
Poincaré, [https://archive.org/details/wissenschaftundh00poin
"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L.
Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice
Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
grundsätzlich anerkannt ("''Sub specie aeterni hat Poincaré mit dieser
Auffassung nach meiner Meinung Recht''"). Demzufolge ist es möglich, die nichteuklidische Geometrie der allgemeinen Relativitätstheorie nicht
Raum und Zeit selbst, sondern gravitativ beeinflussten Maßstäben, Uhren
und allen anderen realen physikalischen Objekten zuzuschreiben und
ansonsten die [[wikipedia-de:Euklidische Geometrie|euklidische Geometrie]] zur
vollständigen Beschreibung des Naturgeschehens beizubehalten. Das
gelingt mit Hilfe einer von [[wikipedia-de:Nathan Rosen|Nathan Rosen]] formulierten ''bimetrischen Relativitätstheorie'' (bi-metric relativity)<ref>N. Rosen,
"''Flat-Space Metric in General Relativity Theory''", Ann. of Physics
22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>. Eine
solche Möglichkeit würde andererseits auch erklären, warum es bisher
trotz großer Anstrengungen ([[wikipedia-de:Stringtheorie|Stringtheorie]],
[[wikipedia-de:Schleifenquantengravitation|Schleifenquantengravitation]]) nicht überzeugend gelungen scheint, die ''[[wikipedia-de:Raumzeit|Raumzeit]]'' zu quantisieren und so die in herkömmlichem Sinne
verstandene [[wikipedia-de:Relativitätstheorie|Relativitätstheorie]] grundsätzlich mit der
[[wikipedia-de:Quantenmechanik|Quantenmechanik]] in einer [[wikipedia-de:allgemeine Relativitätstheorie#Quantenphysik|einheitlichen Theorie von Gravitation und Quantenmechanik]] zu vereinbaren.
Gemäß SUM-Ansatz aber scheint eine Vereinheitlichung prinzipiell möglich, um künftig gültige Aussagen zu
andernfalls bloßen mathematischen [[wikipedia-de:Singularität (Astronomie)|Singularitäten]] der allgemeinen Relativitätstheorie
überhaupt machen zu können, oder wenigstens Fehldeutungen zu verhindern. Dies betrifft neben der Theorie ''[[wikipedia-de:allgemeine Relativitätstheorie#Schwarze Löcher|schwarzer Löcher]]'' auch die
[[wikipedia-de:Singularitäten-Theorem|Singularitätstheoreme]] von [[wikipedia-de:Stephen Hawking|Hawking]] und [[wikipedia-de:Roger Penrose|Penrose]], bei denen in
Ermangelung einer konsistenten Theorie die tatsächliche Quantenstruktur
der Materie bisher außer acht bleiben musste.

== Numerische Hinweise auf die Existenz von 24 elementaren Spin-½ Torsionsteilchen ==

Obwohl mit dem Äquivalenzprinzip in seiner bisherigen Form unvereinbar,
gibt es einen klaren Hinweis auf die Materialisation eines
antisymmetrischen Windungstensors <math>T_{ikl}</math>. Das
Universum scheint demzufolge aus 24 Sorten von Spin-1/2 Partikeln
zusammengesetzt, nämlich aus 6 Arten von Leptonen plus 3 Farben mal 6
Sorten Quarks. Dies entspricht gerade den 24 Komponenten eines
Windungstensors, von denen 6 als 'zeitlich' plus 3*6 als 'räumlich' zu
bezeichnen sind:

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

Schon vor langer Zeit haben Landau & Lifschitz gezeigt, dass die
reale Existenz eines Windungstensors dem Einstein'schen
Äquivalenzprinzip widrsprechen müsste, welches der geometrischen
Interpretation seiner Gravitationsgleichungen zugrundeliegt.
Demgegenüber scheitert der Versuch aus Sicht von SUM, di Physik auf
Riemannsche Eigenschaften einer nicht-Euklidischen 'Raumzeit'
zurückzuführen. Damit scheitert letztlich auch die gesamte
Big-Bang-Kosmologie.

Im Hinblick auf ausgedehnte elementare Spin-1/2-Strukturen (die sich in
den meisten Situationen identfizierbar als ganze verhalten) werden auch
Heisenbergs Unchärferelationen verständlich, ganz im Unterschied zum
Verhalten ansonsten bisher unrealistischerweise vorausgesetzter
'Punkt-Teilchen' wie z.B. Elektronen oder Protonen. Diese sind keine
ausdehnungslosen 'Massen-Punkte' sondern natürlich aausgegdehnte
deformierbare Strukturen mit Teilchen-Parametern in Form konstanter
Integrale für u.a. Spin, Ladung, Ruhemasse. Insbesondere die
quantenmechanische Tatsaache, dass Teilchen im allgemeinen keinen
scharfen Impuls haben, ist angesichts relativer innerer Verschiebungen
ledigkich eine natürliche Feststellung.

Das Torsionskonzept ist unabhängig von der Frage, ob solche Teilchen als materielle Objekte im Vakuum existieren oder in Form von
Wirbelstrukture in einem kontinuierlich ausgedehnten Medium. Die Natur
kann beide Aspekte zeigen (wie bei Spiralnebeln in einem Hintergrund
dunkler Materie).
Die folgende Möglichkeit scheint ''evident'': 
– Elementarteilchen sind Wirbelstrukturen. 
– Aufgrund des Drehimpulserhaltungssatzes sind die winzig
ausgedehnten freien Wirbelstrukturen teilweise über
astronomische Zeiträume beständig. 
– Wirbelstrukturen unterliegen Entstehungs- und
Vergehungsprozessen. 
– In Übergangsphasen verlieren Wirbelstrukturen ihre
Identität. 
– Wirbelstrukturen lassen sich in einer Hinsicht
näherungsweise beschreiben als Teilchen. 
– Wirbelstrukturen lassen sich in anderer Hinsicht
näherungsweise beschreiben als Wellen. 
– In Wirbelstrukturen sind detaillierte Geschwindigkeiten ihrer
Bestandteile und die statistischen Geschwindigkeiten der
jeweiligen Schwerpunktbewegung gleichzeitig realisiert,
woraus sich ganz natürlich Unschärfebeziehungen ergeben. 
Demnach scheinen die Elementarteilchen, aus denen das gesamte Universum
aufgebaut ist, wesentlich verschieden von jenen ewigen festen 'Atomen'
der bahnbrechenden antiken Philosophen Leukipp und Demokrit. Nachdem
klar ist, dass Torsionspartikel nur um den Preis unvermeidlicher
Unschärfen als audehnungslose Punktteilchen behandelt werden dürfen,
muss eine vollständige relativistische Mechanik zukünftig eine
konsistente Formulierung der Quantenmechanik enthalten. Eine geeignete
Basis dafür bietet Rosens 'bi-metrische' Formulierung der
Relativitätstheorie, nachdem sie nun in das (ausgezeichnete) universale
Bezugssystem eingebunden ist.

== Historisches, SUM-Vorläufer, verschiedene verwandte Ansätze ==

Es ist ganz unmöglich, Kosmologie zu betreiben ohne geeignete
Prinzipien, welche - neben der unverzichtberen Verträglichkeit mit
eindeutigen Beobachtungstatsachen - die Kriterien von Einfachheit,
Angemessenheit und Klarheit zu erfüllen haben. Ohne solche Kriterien
wäre gemäß Allgemeiner Relativitätstheorie aufgrund legitimer
Koordinatentransformaionen heute nicht einmal mehr die kopernikanische
Entscheidung zwischen einem heliozentrischen und einem geozentrischen
Planetensystem eindeutig möglich.

Albert Einstein ist bei seiner Begründung der relativistischen
Kosmologie<ref>A. Einstein,
"''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''",
Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref> von der
Voraussetzung eines ewigen Universums ausgegangen. Dieser Versuch ist
daran gescheitert, dass er eine rein ''statische'' Lösung gesucht hat,
deren Linienelement – im Unterschied zu dem Linienelement [[wikipedia-de:Alexander Alexandrowitsch Friedmann|Friedmanns]] wie auch zu demjenigen des
stationären Ansatzes SUM – eine Zeitkoordinate in den entsprechenden
Gravitationspotentialen ''gik'' nicht enthält.
Dies galt auch für die ursprüngliche Form des [[wikipedia-de:De-Sitter-Modell|De-Sitter-Modell]]s, die sich aber durch bloße Koordinatentransformation in das Linienelement
der späteren Steady-State-Theorie überführen ließ.

* Steady-State-Theorie: Unter dem Namen [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]], die eine beständige Expansion beschreiben sollte, wurde im Jahr 1948 ein später (in unterschiedlichen Versionen) an Beobachtungstatsachen gescheitertes Modell des Universums präsentiert, das nach Auffassung seiner Autoren aufgrund ständiger Schöpfung aus dem Nichts als von gleichbleibender Materiedichte erfüllt anzusehen war. Erst in jüngster Zeit wurde bekannt, dass bereits Einstein das Konzept dieser Theorie im wesentlichen vorweggenommen und verworfen hat. Im Unterschied zu SUM wird hier eine ständige Schöpfung aus dem Nichts beschrieben, wobei sich ein von [[wikipedia-de:Fred Hoyle|Fred Hoyle]] eingeführtes ''C''-Feld als Vorläufer des Skalarfeldes des heutigen Inflationsmodells verstehen lässt. Die Rotverschiebungswerte jeweiliger Galaxien ergeben sich in der [[wikipedia-de:Steady-State-Theorie|Steady-State-Theorie]] nicht statistisch konstant, sondern würden entsprechend den zitierten Titeln jener Arbeiten (mit ausdrücklichem Bezug auf ein ''expandierendes Universum'') ständig zunehmen.

* Coasting Cosmology: Ein Modell mit allgemeinerer als der oben angegebenen FLRW-Form des SUM-Linienelements – jedoch mit [[wikipedia-de:Skalenfaktor|Skalenfaktor]] ''HT'' – wurde seinerzeit unter dem Aspekt einer ''gleitenden'' Expansion des Universums diskutiert<ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, bevor 2011 (und später) ein
eng damit verwandtes Konzept noch einmal im Kontext der [[wikipedia-de:Urknall|Urknall-Kosmologie]] behandelt wurde<ref>F. Melia & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The
Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Beide unterscheiden sich grundsätzlich von SUM (die fundamentale Konsequenz gleichbleibender Rotverschiebungswerte von Quellen in gleichbleibenden universalen Entfernungen wurde nicht erwähnt).

* Chaotic Inflation: Der Physiker [[wikipedia-de:Andrei Dmitrijewitsch Linde|Andrei Linde]] hat das Konzept einer [[wikipedia-de:Urknall#chaotische Inflation|chaotischen Inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> entwickelt und dabei die theoretische Fixierung auf einen einzigen Urknall aus dem Nichts effektiv aufgehoben. Andererseits wird dort von ''Parallel''-Universen gesprochen, wovon jedes mit eigener Inflation und gegebenenfalls eigenen Naturgesetzen entstanden sei. Zu den Grundvoraussetzungen von SUM – viele kosmische Bereiche in einem einzigen Universum mit überall gleichen Naturgesetzen – steht das in klarem Widerspruch. In diesem Zusammenhang (obwohl in völlig anderem mathematischen Kontext) ist auch der Begriff 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> erstmalig aufgetaucht.

Hinsichtlich eines ewig im Wandel befindlichen Universums hat es
offenbar schon immer entsprechende Vorstellungen gegeben. Diese scheinen verwandt zum [[wikipedia-de:Samsara|Kreislauf von Werden und Vergehen]] in östlichen Religionen. Nach Auffassung [[wikipedia-de:Epikur|Epikur]]s existieren in einem unendlich
großen Raum eine unendliche Anzahl von Welten. Darüber wurde von Lukrez
in ''[[wikipedia-de:De rerum natura|Über die Natur der Dinge]]'' berichtet. Gemäß
[[wikipedia-de:Rhazes|Rhazes]] sollen – im Sinne zeitloser Naturgesetze – eine ewige Materie aus Atomen, eine absolute und ewige (im Unterschied zur 'geschaffenen'
Welt aber relative) Zeit sowie ein absoluter und ewiger (im Unterschied
zur 'geschaffenen' Welt aber relativer) Raum unveränderlich vorgegeben
sein. Ähnliche Konzepte von Raum und Zeit finden sich später bei Newton. [[wikipedia-de:Nikolaus von Kues|Nikolaus von Kues]] hat sich eine [[wikipedia-de:Parallelwelt|Vielheit von Welten]] in einem einzigen unbegrenzten Universum gedacht. Die im Sinne
moderner Naturwissenschaft neubelebte Vorstellung eines ewigen
unendlichen [[wikipedia-de:Universum|Universum]]s aber existiert spätestens seit
[[wikipedia-de:Thomas Digges|Thomas Digges]]. Sein Zeitgenosse [[wikipedia-de:Giordano Bruno|Giordano Bruno]] verteidigte die Idee
''vieler Welten'', wie insbesondere aus seiner Schrift ''Über die
Unendlichkeit, das Universum und die Welten'' von 1584 hervorgeht (der
Wortwahl dieses Titels entspricht auch die SUM-Unterscheidung von
''Universum'' und ''Kosmen''). Er hatte dabei die Vorstellung, dass das
[[wikipedia-de:Giordano Bruno#Unendlichkeit des Weltalls|ewige unendliche Universum]] ''von demselben göttlichen Puls durchwirkt'' sei. Sein Denken wurde
von den genannten Vorgängern beeinflusst. Im Rahmen von SUM wurde nun
gezeigt, dass sich entsprechende Konzepte nicht nur mit Einsteins
Gleichungen vereinbaren lassen, sondern sich aus diesen zu ergeben
scheinen. Einerseits wird zwar dieses neue Modell von der
Mainstream-Kosmologie bisher kaum wahrgenommen, doch andererseits
scheint das aktuelle ''Konkordanzmodell'' mit seiner teilweise
hochspekulativen (durch keine experimentelle Erfahrung konkret
begründeten, aber dort unverzichtbaren)
''[[wikipedia-de:Inflation (Kosmologie)|Inflationsphase]]'' bei nicht wenigen Menschen auf
zunehmende Skepsis zu stoßen.

Die Idee von SUM - als der einzigen diskutablen Alternative der
originalen Gravitationsleichungen Einsteins ohne kosmologische Konstante - ist, dass keine univeralen Horizonte die physsikalische Realität
beschränken dürfen. Außerhalb ihrer lokalen Anwendbarkeit erweisen sich
alle Konzepte der Speziellen Relativitätsteorie im Rahmen der
konventionell verstandenen Allgemeinen Relativitätsteorie als
überinterpretiert. Deshalb braucht SUM eine wissenschaftliche Diskussion statt endloser Scheingefechte gegen längst überholte historische
Versuche wie der alten SST. Kosmologische Theorien sind nicht dazu da,
die Natur belehren zu wollen, sondern von ihr zu lernen und sie in
Ehrfurcht und gebotener Bescheidenheit zu beschreiben.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia-de:Kategorie: Kosmologie (Physik)- DEUTSCH|Kategorie: Kosmologie (Physik)- DEUTSCH]] --
[[wikipedia-de:Benutzer:Nimos15|Nimos15]] ([[wikipedia-de:Benutzer Diskussion:Nimos15|Diskussion]]) 12:15, 10 Mar 2018 (CET)

Stationary Universe Model (SUM)

2026-02-21T12:10:39Z

Admin: Sections 12-14

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values ('Hubble Trouble') for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref> <ref>A.G. Riess et al., [http://arxiv.org/abs/1801.01120 "New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant"], [http://dx.doi.org/10.3847/1538-4357/aaadb7 doi:10.3847/1538-4357/aaadb7], [http://arxiv.org/abs/1801.01120 "arxiv:1801.01120"]</ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data <ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM_model|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM [[wikipedia:distance_modulus|distance modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:absolute_magnitude|magnitude]] is represented by ''m'' and the [[wikipedia:brightness|absolute brightness]] of [[wikipedia:type_Ia_Supernova|Supernovae type Ia]] [[wikipedia:cosmic_distance_ladder|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Einstein-de_Sitter_universe|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements <ref>P. Ostermann, [http://independent-research.org/assets/nobel-prize-physics-2011.pdf "The well-earned Nobel Prize for the wrong reason"]</ref>.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:homogeneity_and_heterogeneity|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:gravitational_lense|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:critical_density|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:expansion_of_the_universe|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting those authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Planck spectrum of redshifted microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:dark_matter|'dark matter']]''. This concept may solve two fundamental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:black_body|Planck spectrum]] out of [[wikipedia:redshift|redshifted]] radiation without the hypothesis of a 'big bang' <ref>P. Ostermann, [http://independent-research.org/assets/sum_os14.pdf "Model of a Stationary Background Universe Behind Our Cosmos"], 2013 (chapter 2.8)</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "A microwave background of redshifted radiation within the stationary universe, (chapter 5 of "Problems ... " s. above)"]</ref>.

At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:thermal_radiation|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:acoustic oscillations|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:anisotropy|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:black_body|Planck spectrum]] seems [[wikipedia:falsifiable|falsifiable]] with help of the [[wikipedia:Sunyaev%E2%80%93Zel%27dovich_effect|Sunyaev–Zel'dovich effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM <ref>P. Ostermann, [http://independent-research.org/assets/dm1_peter_ostermann_(ulti).pdf "Homogeneously distributed dark matter of second kind as an alternative to 'dark energy"], Talk MG14 in Rome, also explaining the concept of 24 spin-1/2 torsion particles</ref> <ref>P. Ostermann, [http://independent-research.org/assets/cm2_3_peter_ostermann_(ulti).pdf "The PLANCK 2015 model prediction mismatch of Sunyaev-Zeldovich cluster counts and a universal microwave background composed of redshifted radiation from 'dark' matter"], Talk MG14 in Rome </ref> that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:primordial|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a [[wikipedia:redshift|redshift]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar object|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:effects of self selection|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:big_bang|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:false_vacuum|false vacuum]]'' of ''[[wikipedia:quantum fluctuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:big_bang|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:chaotic_inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:graviational_equations|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active_galaxy_nuclei|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:gamma-ray|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Second_law_of_thermodynamics|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:thermodynamics|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:big_bang|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:inflation_(cosmology)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:inflation_(cosmology|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter_asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:big_bang|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble's law|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:anthropic_principle|anthropic principle]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems further to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:general relativity|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:non-euclidean geometry|non-euclidean geometry]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia:euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in [[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]] no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:unified_theory|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:singularity|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:black_holes|black holes]]'' this also concerns the [[wikipedia:Penrose%E2%80%93Hawking_singularity_theorems|singularity theorems]] of [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Sir Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor_(cosmology)|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Linde|Andrei Linde]] has developed the concept of [[wikipedia:eternal_inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been correspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epicurus|Epicurus]] there exists an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:plurality_of_worlds|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. This insight goes back to a seminal analysis ""Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"" of Einstein's ideas<ref>P. Ostermann, [http://arxiv.org/abs/gr-qc/0208056 "Die Einweg-Lichtgeschwindigkeit auf der rotierenden Erde und die Definition des Meters"]</ref>. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.

== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T11:50:25Z

Admin: Sections 9-11

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values ('Hubble Trouble') for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref> <ref>A.G. Riess et al., [http://arxiv.org/abs/1801.01120 "New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant"], [http://dx.doi.org/10.3847/1538-4357/aaadb7 doi:10.3847/1538-4357/aaadb7], [http://arxiv.org/abs/1801.01120 "arxiv:1801.01120"]</ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data <ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM_model|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM [[wikipedia:distance_modulus|distance modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:absolute_magnitude|magnitude]] is represented by ''m'' and the [[wikipedia:brightness|absolute brightness]] of [[wikipedia:type_Ia_Supernova|Supernovae type Ia]] [[wikipedia:cosmic_distance_ladder|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Einstein-de_Sitter_universe|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements <ref>P. Ostermann, [http://independent-research.org/assets/nobel-prize-physics-2011.pdf "The well-earned Nobel Prize for the wrong reason"]</ref>.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:homogeneity_and_heterogeneity|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:gravitational_lense|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:critical_density|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:expansion_of_the_universe|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting those authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Planck spectrum of redshifted microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:dark_matter|'dark matter']]''. This concept may solve two fundamental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:black_body|Planck spectrum]] out of [[wikipedia:redshift|redshifted]] radiation without the hypothesis of a 'big bang' <ref>P. Ostermann, [http://independent-research.org/assets/sum_os14.pdf "Model of a Stationary Background Universe Behind Our Cosmos"], 2013 (chapter 2.8)</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "A microwave background of redshifted radiation within the stationary universe, (chapter 5 of "Problems ... " s. above)"]</ref>.

At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:thermal_radiation|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:acoustic oscillations|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:anisotropy|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:black_body|Planck spectrum]] seems [[wikipedia:falsifiable|falsifiable]] with help of the [[wikipedia:Sunyaev%E2%80%93Zel%27dovich_effect|Sunyaev–Zel'dovich effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM <ref>P. Ostermann, [http://independent-research.org/assets/dm1_peter_ostermann_(ulti).pdf "Homogeneously distributed dark matter of second kind as an alternative to 'dark energy"], Talk MG14 in Rome, also explaining the concept of 24 spin-1/2 torsion particles</ref> <ref>P. Ostermann, [http://independent-research.org/assets/cm2_3_peter_ostermann_(ulti).pdf "The PLANCK 2015 model prediction mismatch of Sunyaev-Zeldovich cluster counts and a universal microwave background composed of redshifted radiation from 'dark' matter"], Talk MG14 in Rome </ref> that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:primordial|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a [[wikipedia:redshift|redshift]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar object|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:effects of self selection|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:big_bang|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:false_vacuum|false vacuum]]'' of ''[[wikipedia:quantum fluctuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:big_bang|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:chaotic_inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:graviational_equations|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active_galaxy_nuclei|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:gamma-ray|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Second_law_of_thermodynamics|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:thermodynamics|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:big_bang|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:inflation_(cosmology)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:inflation_(cosmology|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter_asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:big_bang|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble's law|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:anthropic_principle|anthropic principle]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems further to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T11:27:35Z

Admin: Sections 6-8

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref> <ref>A.G. Riess et al., [http://arxiv.org/abs/1801.01120 "New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant"], [http://dx.doi.org/10.3847/1538-4357/aaadb7 doi:10.3847/1538-4357/aaadb7], [http://arxiv.org/abs/1801.01120 "arxiv:1801.01120"]</ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data <ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM_model|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM [[wikipedia:distance_modulus|distance modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:absolute_magnitude|magnitude]] is represented by ''m'' and the [[wikipedia:brightness|absolute brightness]] of [[wikipedia:type_Ia_Supernova|Supernovae type Ia]] [[wikipedia:cosmic_distance_ladder|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Einstein-de_Sitter_universe|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements <ref>P. Ostermann, [http://independent-research.org/assets/nobel-prize-physics-2011.pdf "The well-earned Nobel Prize for the wrong reason"]</ref>.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:homogeneity_and_heterogeneity|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:gravitational_lense|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:critical_density|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:expansion_of_the_universe|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting those authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:Dunkle Materie|'dark matter']]''. This concept may solve two fundameental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] out of [[wikipedia:Rotverschiebung|redshifted]] radiation without the hypothesis of a 'big bang'.
At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:Wärmestrahlung|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:Baryonische akustische Oszillation|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:Anisotropie|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:Planck spectrum|Planck spectrum]] seems [[wikipedia:Falsifikationismus|falsifiable]] with help of the [[wikipedia:Sunjajew-Seldowitsch effect|Sunjajew-Seldowitsch effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:Primordiale Nukleosynthese|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a redshift [[wikipedia:Rotverschiebung|Rotverschiebung]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar objects|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:Selbstselektion|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:Urknall|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:Vakuumenergie|false vacuum]]'' of ''[[wikipedia:Vakuumfluktuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:Urknall|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:Urknall#chaotische Inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:Einsteinsche Feldgleichungen|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active Galaxienkern|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:Gammablitz|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Entropie#Zweiter Hauptsatz|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:Wärmetod (Physik)|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)#emergence from nothing?| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:Urknall|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:Inflation (Kosmologie)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:Inflation (Kosmologie)#Felddynamik|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:Urknall|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble parameter|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:Anthropisches Prinzip|anthropic prinziple]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems fürther to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T11:13:02Z

Admin: Intro paragraph wiki links

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einstein_field_equations|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]] <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref> <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref> without [[wikipedia:cosmological_constant|''cosmological constant'']] and physically formulated as a reasonable alternative <ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:big_bang|''big bang model'']].
It has been presented at the 12. [[wikipedia:ICRANet|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:standard_model|standard model]] (''Concordance Model'') in form of the [[wikipedia:inflation_(cosmology)|inflationary]] [[wikipedia:Lambda-CDM_model|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady_State_Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:big_bang|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:big_bang|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:cosmological_principle|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:redshift|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euclid|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Comoving_and_proper_distances#comoving_coordinates|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:cosmic_background_radiation|background radiation]] with [[wikipedia:Planck_spectrum|Planck spectrum]] without reduction to a fictional [[wikipedia:big_bang|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data
<ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM-Modell|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM-[[wikipedia:Absolute Helligkeit|distsnce modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:Scheinbare Helligkeit|magnitude]] is represented by ''m'' and the [[wikipedia:Absolute Helligkeit|absolute brightnes]] of [[wikipedia:Supernova vom Typ Ia|Supernovae type Ia]] (SNe-Ia) as [[wikipedia:Standardkerze|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:Inhomogenität|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:Gravitationslinseneffekt|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:Kritische Dichte|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:Expansion des Universums|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting the authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:Dunkle Materie|'dark matter']]''. This concept may solve two fundameental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] out of [[wikipedia:Rotverschiebung|redshifted]] radiation without the hypothesis of a 'big bang'.
At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:Wärmestrahlung|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:Baryonische akustische Oszillation|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:Anisotropie|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:Planck spectrum|Planck spectrum]] seems [[wikipedia:Falsifikationismus|falsifiable]] with help of the [[wikipedia:Sunjajew-Seldowitsch effect|Sunjajew-Seldowitsch effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:Primordiale Nukleosynthese|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a redshift [[wikipedia:Rotverschiebung|Rotverschiebung]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar objects|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:Selbstselektion|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:Urknall|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:Vakuumenergie|false vacuum]]'' of ''[[wikipedia:Vakuumfluktuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:Urknall|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:Urknall#chaotische Inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:Einsteinsche Feldgleichungen|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active Galaxienkern|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:Gammablitz|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Entropie#Zweiter Hauptsatz|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:Wärmetod (Physik)|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)#emergence from nothing?| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:Urknall|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:Inflation (Kosmologie)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:Inflation (Kosmologie)#Felddynamik|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:Urknall|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble parameter|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:Anthropisches Prinzip|anthropic prinziple]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems fürther to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T11:07:01Z

Admin: Sections 3-5

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einsteinsche Feldgleichungen|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]]
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref>
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref>
without [[wikipedia:kosmologische Konstante|''cosmological constant'']] and physically formulated as a reasonable alternative
<ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:Urknall#Expansion des Universums|''big bang model'']].
It has been presented at the 12. [[wikipedia:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:Kosmologie|standard model]] (''Concordance Model'') in form of the [[wikipedia:Inflation (Kosmologie)|inflationary]] [[wikipedia:Lambda-CDM-Modell|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady State Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:Expansion des Universums|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:Urknall|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:Kosmologisches Prinzip|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:Rotverschiebung|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euklidische Geometrie|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Entfernungsmaß#Mitbewegte Entfernung|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:Hintergrundstrahlung|background radiation]] with [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] without reduction to a fictional [[wikipedia:Urknall|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:spontan_emission|spontan emission]] and subsequent [[wikipedia:absorption_(physics)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble_time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper_length|proper length]]'' and ''[[wikipedia:proper_time|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann–Lemaître–Robertson–Walker_metric|Friedmann-Lemaître-Robertson-Walker form (FLRW form)]] with the simplest [[wikipedia:scale factor_(cosmology)|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#|''covariant'']] Einstein tensor - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:mixed_tensor|mixed tensor]] component ''G''00, which would apply at application of [[wikipedia:Einstein_field_equations|gravitational equations]] on local [[wikipedia:perfect_fluids|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:proper_times|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:critical_density_(cosmology)|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:diffusion|diffuse]] without its walls), galaxies within a limited region of the stationary universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data
<ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM-Modell|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM-[[wikipedia:Absolute Helligkeit|distsnce modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:Scheinbare Helligkeit|magnitude]] is represented by ''m'' and the [[wikipedia:Absolute Helligkeit|absolute brightnes]] of [[wikipedia:Supernova vom Typ Ia|Supernovae type Ia]] (SNe-Ia) as [[wikipedia:Standardkerze|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:Inhomogenität|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:Gravitationslinseneffekt|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:Kritische Dichte|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:Expansion des Universums|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting the authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:Dunkle Materie|'dark matter']]''. This concept may solve two fundameental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] out of [[wikipedia:Rotverschiebung|redshifted]] radiation without the hypothesis of a 'big bang'.
At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:Wärmestrahlung|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:Baryonische akustische Oszillation|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:Anisotropie|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:Planck spectrum|Planck spectrum]] seems [[wikipedia:Falsifikationismus|falsifiable]] with help of the [[wikipedia:Sunjajew-Seldowitsch effect|Sunjajew-Seldowitsch effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:Primordiale Nukleosynthese|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a redshift [[wikipedia:Rotverschiebung|Rotverschiebung]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar objects|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:Selbstselektion|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:Urknall|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:Vakuumenergie|false vacuum]]'' of ''[[wikipedia:Vakuumfluktuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:Urknall|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:Urknall#chaotische Inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:Einsteinsche Feldgleichungen|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active Galaxienkern|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:Gammablitz|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Entropie#Zweiter Hauptsatz|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:Wärmetod (Physik)|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)#emergence from nothing?| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:Urknall|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:Inflation (Kosmologie)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:Inflation (Kosmologie)#Felddynamik|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:Urknall|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble parameter|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:Anthropisches Prinzip|anthropic prinziple]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems fürther to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T10:56:36Z

Admin: Sections 1 & 2

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einsteinsche Feldgleichungen|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]]
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref>
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref>
without [[wikipedia:kosmologische Konstante|''cosmological constant'']] and physically formulated as a reasonable alternative
<ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:Urknall#Expansion des Universums|''big bang model'']].
It has been presented at the 12. [[wikipedia:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:Kosmologie|standard model]] (''Concordance Model'') in form of the [[wikipedia:Inflation (Kosmologie)|inflationary]] [[wikipedia:Lambda-CDM-Modell|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady State Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:Expansion des Universums|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:Urknall|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:Kosmologisches Prinzip|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:Rotverschiebung|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euklidische Geometrie|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Entfernungsmaß#Mitbewegte Entfernung|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:Hintergrundstrahlung|background radiation]] with [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] without reduction to a fictional [[wikipedia:Urknall|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:axiom|postulates]] are sufficient to derive SUM's stationary [[wikipedia:line_element|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble_constant| Hubble parameter]]
''H''0 of the [[wikipedia:big_bang|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:special_relativity|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:comoving_coordinates|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:proper_length|proper lengths]] and the [[wikipedia:proper_time|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:speed_of_light|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:galaxy|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler_effect|Doppler effect]] but in sense of an extended Einsteinian [[wikipedia:gravitational_redshift|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound–Rebka_experiment|Pound and Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]] <ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:gravitational_redshift|gravitational redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Redshift|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:proper_length|proper lengths]] due to the constant values of redshift of corresponding objects <ref>P. Ostermann, [http://independent-research.org/assets/hubble_os14.pdf" A Strange Detail Concerning the Conceptualization of the Hubble Constant"]</ref>. Contrary to [[wikipedia:big_bang|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:Spontane Emission|emission]] and subsequent [[wikipedia:Absorption (Physik)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper length|proper length]]'' and ''[[wikipedia:Zeitdilatation#Eigenzeit|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann-Lemaître-Robertson-Walker-Metrik|Friedmann-Lemaître-Robertson-Walker-Form (FLRW-Form)]] with the simplest [[wikipedia:scale factor|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#Ko- und Kontravarianz|''covariant'']] [[wikipedia:Friedmann-Gleichung#Herleitung|Einstein-Tensor]] - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:Krummlinige Koordinaten#Tensoren zweiter Stufe|mixed co- contravariant]] component ''G''00, which would apply at application of [[wikipedia:Einsteinsche Feldgleichungen|gravitational equations]] on local [[wikipedia:Ideale Flüssigkeit|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:Zeitdilatation#Eigenzeit|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:kritische Dichte|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:Diffusion|diffuse]] without its walls), galaxies within a limited region of the stationaty universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data
<ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM-Modell|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM-[[wikipedia:Absolute Helligkeit|distsnce modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:Scheinbare Helligkeit|magnitude]] is represented by ''m'' and the [[wikipedia:Absolute Helligkeit|absolute brightnes]] of [[wikipedia:Supernova vom Typ Ia|Supernovae type Ia]] (SNe-Ia) as [[wikipedia:Standardkerze|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:Inhomogenität|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:Gravitationslinseneffekt|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:Kritische Dichte|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:Expansion des Universums|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting the authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:Dunkle Materie|'dark matter']]''. This concept may solve two fundameental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] out of [[wikipedia:Rotverschiebung|redshifted]] radiation without the hypothesis of a 'big bang'.
At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:Wärmestrahlung|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:Baryonische akustische Oszillation|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:Anisotropie|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:Planck spectrum|Planck spectrum]] seems [[wikipedia:Falsifikationismus|falsifiable]] with help of the [[wikipedia:Sunjajew-Seldowitsch effect|Sunjajew-Seldowitsch effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:Primordiale Nukleosynthese|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a redshift [[wikipedia:Rotverschiebung|Rotverschiebung]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar objects|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:Selbstselektion|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:Urknall|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:Vakuumenergie|false vacuum]]'' of ''[[wikipedia:Vakuumfluktuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:Urknall|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:Urknall#chaotische Inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:Einsteinsche Feldgleichungen|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active Galaxienkern|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:Gammablitz|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Entropie#Zweiter Hauptsatz|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:Wärmetod (Physik)|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)#emergence from nothing?| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:Urknall|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:Inflation (Kosmologie)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:Inflation (Kosmologie)#Felddynamik|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:Urknall|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble parameter|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:Anthropisches Prinzip|anthropic prinziple]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems fürther to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-21T10:44:19Z

Admin: Intro paragraph

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einsteinsche Feldgleichungen|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]]
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref>
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref>
without [[wikipedia:kosmologische Konstante|''cosmological constant'']] and physically formulated as a reasonable alternative
<ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref> <ref>P. Ostermann, [http://independent-research.org/assets/altern16.pdf "Problems of single-bang cosmology from the perspective of the mathematically simplest alternative based on Einstein's equations"]</ref> <ref>P. Ostermann, [https://web.archive.org/web/20230326205344/http://independent-research.org/assets/multiverse_18.pdf "New physics of an eternal infinite multiverse instead of today's singular big-bang cosmology"], preprint 2018</ref> to the numerically utmost successful [[wikipedia:Urknall#Expansion des Universums|''big bang model'']].
It has been presented at the 12. [[wikipedia:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230 Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints are at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:Kosmologie|standard model]] (''Concordance Model'') in form of the [[wikipedia:Inflation (Kosmologie)|inflationary]] [[wikipedia:Lambda-CDM-Modell|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated [[wikipedia:Steady State Theory|Steady State Theory]] seems compatible to current observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think) and seems almost a miracle, that on basis of Einstein's equations the idea of an infinite stationary universe turns out to imply clear indication that individual cosmoses are of finite dimensions in space and time. It is in particular this conclusion that arises from the interplay of local special relativity (macroscopically representing quantum mechanics) and universal general relativity (representing gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a stationary multiverse – the same mathematical model is bringing ideas of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses. While these ideas seem implausibly unbalanced in the prevailing western single-bang standard approach, the new concept SUM, if understood in sense of a Tao Cosmology, seems naturally incorporated into the picture of a multiverse as an oscillation of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

After the science-fiction breaking Hossenfelder wake-up call <ref>S. Hossenfelder: "Lost in Math", Basic Books, New York 2018</ref> , the central question remains: What does the dilemma of today's mainstream physics mean in reality? Conclusions from SUM – completely new in contrast to the fictitiously asssumed big bang – allow for a solution in principle of the most puzzling questions of today's Lambda-CDM Concordance Cosmology, which after a paradigm shift to SUM might be resolved at one blow:

* matter-antimatter baryon asymmetry – is a natural fact in a stationary universe without need for justification.
* cosmological redshift without universal spatial expansion due to another kind of ordinary gravitational redshift
* 'dark energy' – homogeneous distribution of e.g. neutrinos (or other WIMPs) filling the gap to critical density
* dark matter – neutrinos (thermalized in parts)
* SNeIa magnitude vs. resdshift measurements ...
* requiring two Hubble 'constants' (the local and the universal one) instead of an accelerated expansion ('Hubble trouble')
* Planck spectrum from a black-body background of redshifted microwave radiation emitted within a non-expanding multiverse
* the law of entropy restricted to evolutionary processes (without conflict against any laboratory experience – time after time allowing for 'primordial' nucleosynthesis in 'multi bang' processes of re-creation)
* SUM may describe a local-bang 'multiverse' (which is just another word for actually one universe with multiple cosmoses).

Team leader and Nobel Laureate Adam Riess' comment on the 'Hubble trouble': ''"The tension seems to have grown into a full-blown incompatibility between our views of the early and late time universe" (July 12, 2018 at <nasa.gov/feature/goddard/2018/hubble-and-gaia-team-up-to-fuel-cosmic-conundrum>). “At this point, clearly it’s not simply some gross error in any one measurement. It’s as though you predicted how tall a child would become from a growth chart and then found the adult he or she became greatly exceeded the prediction. We are very perplexed [...] The tension could thus provide evidence of physics beyond the standard model (or unaccounted systematic errors) [...] These recent results clearly motivate a detailed study of possible extensions of the Lambda-CDM model and an inspection of the current cosmological data sets, checking for inconsistencies."''

According to recently found limitations of proper length and proper time the Hubble radius is setting an uppermost limit for the validity of any approximate SRT concepts and processes transferred to cosmology. Thus the new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Immanuel Kant]]'s first antinomy of space and time – does neither include an [[wikipedia:Expansion des Universums|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:Urknall|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:Kosmologisches Prinzip|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:Rotverschiebung|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euklidische Geometrie|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Entfernungsmaß#Mitbewegte Entfernung|comoving coordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:Hintergrundstrahlung|background radiation]] with [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] without reduction to a fictional [[wikipedia:Urknall|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013) <ref>P. Ostermann, "Model of a Stationary Background Universe Behind Our Cosmos", 2014 [equation (9) here ok]</ref>. The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:Postulat|postulates]] are sufficient to derive SUM's stationary [[wikipedia:Metrischer Tensor#Linienelement|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble-Konstante#Definition| Hubble parameter]]
''H''0 of the [[wikipedia:Urknall|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:Spezielle Relativitätstheorie|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:Entfernungsmaß#Mitbewegte Entfernung|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:Beobachter (Physik)#Relativitätstheorie|proper lengths]] and the [[wikipedia:Zeitdilatation#Eigenzeit|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:Lichtgeschwindigkeit|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:Galaxie|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler-Effekt|Doppler-Effekt]] but in sense of an extended Einsteinian [[wikipedia:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound-Rebka-Experiment|Pound und Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]]
<ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitational Redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Rotverschiebung|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:Beobachter (Physik)#Relativitätstheorie|proper lengths]] due to the constant values of redshift of corresponding objects. Contrary to [[wikipedia:Urknall|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:Spontane Emission|emission]] and subsequent [[wikipedia:Absorption (Physik)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper length|proper length]]'' and ''[[wikipedia:Zeitdilatation#Eigenzeit|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann-Lemaître-Robertson-Walker-Metrik|Friedmann-Lemaître-Robertson-Walker-Form (FLRW-Form)]] with the simplest [[wikipedia:scale factor|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#Ko- und Kontravarianz|''covariant'']] [[wikipedia:Friedmann-Gleichung#Herleitung|Einstein-Tensor]] - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:Krummlinige Koordinaten#Tensoren zweiter Stufe|mixed co- contravariant]] component ''G''00, which would apply at application of [[wikipedia:Einsteinsche Feldgleichungen|gravitational equations]] on local [[wikipedia:Ideale Flüssigkeit|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:Zeitdilatation#Eigenzeit|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:kritische Dichte|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:Diffusion|diffuse]] without its walls), galaxies within a limited region of the stationaty universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data
<ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/ "''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref> on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM-Modell|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM-[[wikipedia:Absolute Helligkeit|distsnce modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:Scheinbare Helligkeit|magnitude]] is represented by ''m'' and the [[wikipedia:Absolute Helligkeit|absolute brightnes]] of [[wikipedia:Supernova vom Typ Ia|Supernovae type Ia]] (SNe-Ia) as [[wikipedia:Standardkerze|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, [http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:Inhomogenität|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:Gravitationslinseneffekt|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:Kritische Dichte|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:Expansion des Universums|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting the authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:Dunkle Materie|'dark matter']]''. This concept may solve two fundameental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] out of [[wikipedia:Rotverschiebung|redshifted]] radiation without the hypothesis of a 'big bang'.
At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:Wärmestrahlung|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:Baryonische akustische Oszillation|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:Anisotropie|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:Planck spectrum|Planck spectrum]] seems [[wikipedia:Falsifikationismus|falsifiable]] with help of the [[wikipedia:Sunjajew-Seldowitsch effect|Sunjajew-Seldowitsch effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:Primordiale Nukleosynthese|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a redshift [[wikipedia:Rotverschiebung|Rotverschiebung]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar objects|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:Selbstselektion|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:Urknall|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:Vakuumenergie|false vacuum]]'' of ''[[wikipedia:Vakuumfluktuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:Urknall|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:Urknall#chaotische Inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:Einsteinsche Feldgleichungen|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active Galaxienkern|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:Gammablitz|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Entropie#Zweiter Hauptsatz|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:Wärmetod (Physik)|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)#emergence from nothing?| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:Urknall|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:Inflation (Kosmologie)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:Inflation (Kosmologie)#Felddynamik|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:Urknall|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble parameter|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:Anthropisches Prinzip|anthropic prinziple]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems fürther to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

Stationary Universe Model (SUM)

2026-02-14T14:31:12Z

Admin: Created page with "<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big> The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original ''field equations'' of wikipedia:Albert Einstein| <ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleic..."

<big><big><big>'''Stationary Universe Model (SUM)'''</big></big></big>

The '''Stationary Universe Model''' ('''SUM''') has been developed as ''work in progress'' by the physicist Peter Ostermann since 2001 from the presuppositon of an eternal, infinite universe on base of the original [[wikipedia:Einsteinsche Feldgleichungen|''field equations'']] of [[wikipedia:Albert Einstein|Albert Einstein]]
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/272 "''Die Feldgleichungen der Gravitation''"], Sitz.ber. Preuß. Akad. Wiss., 25. November 1915, 844-847 – (reprint Doc. 25, CPAE Vol. 6)</ref>
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol6-doc/312 "''Die Grundlage der allgemeinen Relativitätstheorie''"], Ann. d. Phys. 49, 769-822 – (reprint Doc. 30 CPAE Vol. 6)</ref>
without [[wikipedia:kosmologische Konstante|''cosmological constant'']] and physically formulated as a reasonable alternative
<ref>P. Ostermann, "''[http://arXiv.org/abs/physics/0211054 Ein stationäres Universum und
die Grundlagen der Relativitätstheorie]''", arXiv:physics/0211054, 2002/04</ref>
to the numerically utmost successful [[wikipedia:Urknall#Expansion des Universums|''big bang model'']].
It has been presented at the 12. [[wikipedia:Marcel Grossmann Meeting|Marcel Grossmann Meeting]]
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0230
Relativistic Deduction of a Stationary Tohu-va-Bohu Background Cosmology]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1408-1410, 2012; [http://independent-research.org/assets/mg12_cot3_proceed_ostermann.pdf, article PDF 2012]</ref>
<ref>P. Ostermann, "''[http://www.worldscientific.com/doi/abs/10.1142/9789814374552_0219 Indication from the Supernovae Ia Data of a Stationary Background Universe]''"; in: Damour Th., Jantzen R. T., & Ruffini R. (Eds.), Proc. MG12, W.Sci., 1373-1375, 2012; [http://independent-research.org/assets/mg12_cot2_proceed_ostermann.pdf, article PDF 2012]</ref>
in Paris (MG12 2009, and at the DPG-Frühjahrstagung
<ref>P. Ostermann, "''[http://independent-research.org/assets/07a.pdf Das relativistische Modell eines stationären Hintergrunduniversums und die Supernova-Ia-Daten]''"; DPG-Vortrag/GR-205.2, 2007</ref>
2007 Heidelberg before, first pre-prints at arXiv.org).
In comparison with the due to excellent apparent confirmations for a long time prevailing [[wikipedia:Kosmologie|standard model]] (''Concordance Model'') in form of the [[wikipedia:Inflation (Kosmologie)|inflationary]] [[wikipedia:Lambda-CDM-Modell|Lambda CDM cosmology]] is SUM on base of a new line element representing a concept, which in contrast to the outdated Hubble's law [[wikipedia:Steady State Theory|Steady State Theory]] seems compatible to current cosmological observational facts. Despite amazing unexpected successes the model doesn't reach the highly developed stand with regard to various details of the CCM, but is still in an initial phase; it is an encouragement in the sense of clearing up: "sapere aude!" (dare to think).

It seems almost a miracle, that on basis of Einstein's equations the idea of an ''infinite'' stationary universe turns out to imply clear indication that individual
cosmoses are of finite dimensions in space and time. It is in particular
this conclusion that arises from the interplay of local special relativity (macroscopically
representing quantum mechanics) and universal general relativity (representing
gravitation). The unexpected feature is that – describing our evolutionary cosmos as part of a
stationary multiverse – the same mathematical model is bringing ideas
of various cultural areas to mind about existence of an eternal universe and the creation of cosmoses.
While these ideas seem implausibly unbalanced in the prevailing western single-bang
standard approach, the new concept SUM, if understood in sense of an Ubuntu Tao Cosmology,
seems naturally incorporated into the picture of a multiverse as an oscillation
of forces, which might philosophically also be named Yin and Yang. Preliminarily this tries to be a mainstream-breaking attempt to free human spirit from all dogmatic chains unfortunately limiting ubuntu science so far.

The new cosmological model SUM – distinguishing our evolutionary cosmos from the stationary background universe, what also solves [[wikipedia:Kant|Kant]]s first antinomy of space and time – does neither include an [[wikipedia:Expansion des Universums|expansion of space]] nor an end of the universe in bleak emptiness as nowadays usually otherwise predicted. It starts from the physical fact that nothing arises from nothing. The entirety of all is regarded as a consistent reality and in sense of ''stationary universe'' - not at all static - distinguished from our [[wikipedia:Urknall|''evolutionary cosmos'']]. Therefore both its age and its extension are infinite, but this does not apply to our cosmos as part of it.

What in view of the FLRW singularity is otherwise called 'age of the universe', now in view of SUM turns out to be rather the maximum age of macroscopic structures. Seemingly opposite observations of e.g. oldest galaxies cannot convince of a singular origin. This in analogy to the commonplace experience that the existence of people with each member not older than about one hundred years does not prove this individual maximum lifetime to be the age of the whole population. Therefore – in contrast to the natural search for the vital history of our cosmos – it does not make sense to search for a continuous history of the entire universe.

In spite of both presupposing in common the ''[[wikipedia:Kosmologisches Prinzip|perfect cosmological principle]]'' the model SUM with its statistically constant values of [[wikipedia:Rotverschiebung|redshift]] is fundamentally different from the [[wikipedia:Steady State Theory|Steady State Theory]] of an expanding universe
<ref>H. Bondi & T. Gold, [http://adsabs.harvard.edu/full/1948MNRAS.108..252B "''The Steady-State Theory of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 252-270, 1948</ref>
<ref>F. Hoyle, [http://articles.adsabs.harvard.edu/full/1948MNRAS.108..372H "''A New Model of the Expanding Universe''"] Monthly Notices, Royal Astronomical Society, vol. 108, 372-382, 1948</ref>.
The mathematically exactly derived values of redshift correspond to the statistically constant [[wikipedia:Euklidische Geometrie|Euclidean]] distances in universal coordinates which are also called ''[[wikipedia:Entfernungsmaß#Mitbewegte Entfernung|comoving cooordinates]]'' because of historical grounds. After a preliminarly purely mathematical derivation of a stationary [[wikipedia:Hintergrundstrahlung|background radiation]] with [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] without reduction to a fictional [[wikipedia:Urknall|big bang]]) a previous version of SUM
<ref>P. Ostermann, "''[http://arXiv.org/abs/astro-ph/0312655v6 The Concordance Model - a Heuristic Approach from a Stationary Universe]''", arXiv:astro-ph/0312655v6, 2013</ref>
has been developed to ''Model of a Stationary Background Universe Behind Our Cosmos'' (2013). The underlying articles are at [http://independent-research.org "independent-research.org"] ready for download.

== The stationary line element ==

[[File:SUM scale factor.jpg|thumb|'''''Fig. W1'''''. – The assignments (<math>\Omega_\mathrm{M}</math>, <math>w_\mathrm{M}</math>, <math>\Omega_\mathrm{\Lambda}</math>) = (0, 0, 1), (0.1, 0, 0.9), (0.27, 0, 0.73), (1,–1/3 , 0) , (0.6, 0, 0.4), (1, 0, 0), i.e.:
Steady-state Theory <math>a_\mathrm{SST}(t') = \mathrm{e}^{Ht'}</math> [upper grey solid line], this model discussed as a possible option in the past; a first alternative to <math>a_\mathrm{CCM}(t')</math> with higher value <math>\Omega_\mathrm{\Lambda}</math>) [blue broken line]; today's Concordance Model <math>a_\mathrm{CCM}(t')</math> [blue solid line]; the stationary ultra-large scale universe <math>a_\mathrm{SUM}(t') = HT'</math> = <math>1+Ht'</math> [red straight line]; a second variant to <math>a_\mathrm{CCM}(t')</math> with lower value
<math>\Omega_\mathrm{\Lambda}</math>) [lower blue broken line]; the Einstein-de-Sitter model <math>a_\mathrm{EdS}(t') = </math> <math>(1 + \mathrm{3/2}Ht')^\mathrm{2/3}</math> [lower grey solid line, favored before the SNe-Ia breakthrough]. In contrast to all other comparable values the CCM best-fit parameter <math>\Omega_\mathrm{\Lambda}</math>) = 0.737 (blue solid line) seems determined by the condition, that its line should meet the SUM scalefactor (red) at its boundaries, i.e. at HT' = -1 exactly and at Ht' ≈ 0 approximately today. – SUM's unexpected local character as pseudo-proper FLRW form is concluded according to the corresponding sections above.]]

In contrast to ''static'' the word ''stationary'' means, that all things considered remain at large the same, though single components may permanently change. The concept of SUM can be based on a deductive development different from any inductive conclusion. Two [[wikipedia:Postulat|postulates]] are sufficient to derive SUM's stationary [[wikipedia:Metrischer Tensor#Linienelement|line element]]:

* Postulate I – With respect to sufficiently large scales the universe is stationary, homogeneous and isotropic.
* Postulate II – Except for local deviations the universal speed of light is ''c''* = ''c'' .

From these postulates - both extraordinarily simple - SUM's line element d''σ''*SUM of a spatially flat non-empty universe results uniquely to be
:<math>
\mathrm{d}\sigma_\mathrm{SUM}^{\ast} =
\mathrm{e}^{Ht^{\ast}}\mathrm{d}\sigma_\mathrm{SRT}^{\ast}
</math>.
Here ''H'' stands for a true ''Hubble constant'' (which in contrast to CCM's time-dependent ''conventional'' [[wikipedia:Hubble-Konstante#Definition| Hubble parameter]]
''H''0 of the [[wikipedia:Urknall|big bang cosmology]] is called ''significant''; the abbreviation d''σ''*SRT stands for the line element of [[wikipedia:Spezielle Relativitätstheorie|special relativity]], where the additional symbol '<math>\,</math>*<math>\,</math>' is indicating at each occurance the feature, that corresponding values are related to ''universal coordinates'' (besides '[[wikipedia:Entfernungsmaß#Mitbewegte Entfernung|comoving coordinates]]' ''l''<math>\,</math>* also the 'conformal time'
''t''<math>\,</math>*).

According to SUM the universal coordinates temporarily match the [[wikipedia:Beobachter (Physik)#Relativitätstheorie|proper lengths]] and the [[wikipedia:Zeitdilatation#Eigenzeit|proper times]] of special relativity again an again. From the line element's explicit quadrat written out is the constancy of the universal [[wikipedia:Lichtgeschwindigkeit|speed of light]] obvious because of c* ≡ d''l''<math>\,</math>*/d''t'' * = c (for d''σ''*SUM = 0).

== Redshift and the significant Hubble constant ==

[[File:Hubble-contrast.jpg|thumb|'''''Fig. W2''''' - SUM's prediction of the Hubble contrast which is completely incomprehensible in the framework of Lambda-CDM 'big-bang' cosmology:
Two different values for the Hubble 'costant' <math>H_{\mathrm{local}}</math> = <math>H_{\mathrm{CCM}}</math> and <math>H_{\mathrm{universal}}</math> = <math>H_{\mathrm{SUM}}</math>.

'''''-- Top panel (a)}:''''' The blue solid line does represent the real values <math>z_{\mathrm{observed}}</math> of the SNe-Ia maesurements,the red boken SUM line is peliminarily neglecting possible 'peculiar flows' or local inhomogeneities. The maximum deviation <math>\delta
z</math> ≈ 0.002} ≈ 600 km/s/c within <math>z</math> < 0.027 does correspond too a maximum contrast <math>H_{\mathrm{local}}</math> / <math>H_{\mathrm{universal}}</math> - 1} of about 9% at this distance while <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc.

'''''-- Bottom panel (b)}:'''''Within <math>r^* < 110</math> Mpc the blue line corresponds to <math>H_{\mathrm{local}}</math> ≈ 73 km/s/Mpc, while the mean value in the transition zone (up to <math>z</math> ≈ 0.13) is about <math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc. The difference leads to
<math>H_{\mathrm{local}}/H_{\mathrm{trans}}</math> - 1 ≈ 4.7% up to <math>H_{\mathrm{local}}/H_{\mathrm{universal}}</math> - 1 ≈ 8.9% thus approximately corresponding to the range of the local Hubble contrast reported by Jha, Riess & Kirshner to be 6.5% ± 1.8%.}
]]

It is simply wrong to claim that the cosmic redshift proves any expansion. The ''universal redshift'' of distant
[[wikipedia:Galaxie|galaxies]] is understood in the SUM framework not as a [[wikipedia:Doppler-Effekt|Doppler-Effekt]] but in sense of an extended Einsteinian [[wikipedia:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitational redshift]]. This corresponds exactly to the well-known fact that the redshift once measured by [[wikipedia:Pound-Rebka-Experiment|Pound und Rebka]] is not at all caused by a flight between emitter at the top of the Jefferson tower and a receiver on the ground (even [[wikipedia:Edwin Hubble|Edwin Hubble]]
<ref>E.P. Hubble, [http://www.pnas.org/content/15/3/168.full "''A relation between distance and radial velocity among extra-galactic nebulae''"], Proc. N. Acad. Sci. 15, 168-173, 1929</ref>
had already considered such an alternative explanation instead of a fictive mysterious Doppler effect which would be out of place in this context).

The only difference in comparison with an ordinary [[wikipedia:Rotverschiebung#Gravitative Rot- und Blauverschiebung|gravitational Redshift]] is that in this case the potential takes a time-dependent form, which due to its sign always affects as a ''red shift''. According to the general definition of the [[wikipedia:Rotverschiebung|redshift parameter]] ''z'' = ''λ''<math>\,</math>observed / ''λ''<math>\,</math>emitted – 1 do result with
:<math>
z_{\mathrm{SUM}} = \mathrm e^{Hl^{\ast} / c} - 1
</math>
which like the ''significant'' Hubble constant in the SUM frameword are independent of time. Such values apply to all cosmic structures, which by commonly accepted presupposition are statistically at rest with respect to universal coordinates (''x''*, ''y''*, ''z''*). Thhe independence of time applies to all other quantities which are actual functions of ''z''. In particular the constant universal distances
:<math>
l^{\ast} = \tfrac {c}{H} \ln {(1+z)}
</math>
are real measurands in addition to the local SRT [[wikipedia:Beobachter (Physik)#Relativitätstheorie|proper lengths]] due to the constant values of redshift of corresponding objects. Contrary to [[wikipedia:Urknall|big bang theory]] the universal distance ''l''* is uniquely maesurable - though indirectly - in the SUM framework.

== Universal time ''t''<math>\,</math>* and the limits of proper length and proper time ==

Because of the exponential mean time scalar e''Ht'' *, all corresponding relative temporal changes depend on differences ''t'' * – ''t''R* according to e''Ht'' */ e''Ht''R* = e''H''(''t'' * – ''t''R*) solely, where ''t''R* is a respective reference point of universal time. Therefore no special fixation of the universal time scale ''t'' * is preferred. This fundamental feature is what allows arbitrarily to set ''t''R* = 0 for arbitrary complexes of observation.
The same fact applies to all other coherent events, in particular also to [[wikipedia:Spontane Emission|emission]] and subsequent [[wikipedia:Absorption (Physik)|absorption]] of photons in distant galaxies.

In contrast to the respective local quasi-proper time ''t'' ' = ''T'' ' – ''T''H (where ''T''H = 1/''H'' is the [[wikipedia:Hubble time|Hubble time]]) the universal time ''t'' * has neither a beginnig nor an end. According to the SRT line element remaining locally valid
in any place and ever again (d''σ''2SRT = ''c''2d''t''<math>\,</math>2SRT – d''l''<math>\,</math>2SRT) the intervals of ''[[wikipedia:proper length|proper length]]'' and ''[[wikipedia:Zeitdilatation#Eigenzeit|proper time]]'' are defined always together. From SUM's line element the mathematical approximations are easily concluded yielding
:<math>
\mathrm{d}t_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}t^{\ast}
</math> ,
:<math>
\mathrm{d}l_{\mathrm{SRT}}</math> ≈ <math>\mathrm
e^{Ht^{\ast}}\mathrm{d}l^{\ast}
</math>
to be temporarily valid within locally restricted regions
:<math>
l^{\ast} \ \stackrel{!}{<} \ R_{\mathrm{H}}
</math>
of the infinite Euclidean space (d''l'' 2 =
d''x''<math>\,</math>2 +
d''y''<math>\,</math>2 +
d''z''<math>\,</math>2), where ''R''H =
''c''/''H'' is the [[wikipedia:Beobachtbares Universum#Hubble-Radius|Hubble radius]].
The same applies to each SRT concept at all. If, however, there was perfect equlity in the above approximations with equal signs '=' instead of approximate signs,
the each cosmological line element would be nothing but that of SRT itself – whose Riemann, Ricci, or Einstein tensors and therefore the entire universal mass energy density would mathematically vanish to zero. The last inequality above results after a double ''coordinate transformation''
''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' and ''l'' * = ''l'' '<math>\,</math>/<math>\,</math>(''HT'' '),
where ''T'' ' corresponds approximately to a local ''proper time'', which is limited according to the above inequality respectively.

== The FLRW form of the SUM line element ==

If according to ''t'' * = ln<math>\,</math>(''HT'' ')<math>\,</math>/<math>\,</math>''H'' only the universal time ''t'' * was transformed, it would follow the stationary line element in a
[[wikipedia:Friedmann-Lemaître-Robertson-Walker-Metrik|Friedmann-Lemaître-Robertson-Walker-Form (FLRW-Form)]] with the simplest [[wikipedia:scale factor|scale factor]] ''a''<math>\,</math>SUM = ''HT'' ' yielding
:<math>
\mathrm{d}\sigma_\mathrm{SUM-FLRW}^{\ast 2} =
c^2\mathrm{d}T^{\,\prime\,2} -
(HT^{\, \prime})^2 \mathrm{d}l^{\ast 2}
</math>
without changing any real physical facts. It is easily verified, for example, that from SUM's exact Hubble relation between redshift ''z'' and universal distance ''l''<math>\,</math>* above holds in its time-independent form, too. It is of decisive importance that the singularity ''quasi-proper time T'' ' = 0 of an apparent 'beginning' applies only to locally restricted areas and does not at all represent an age of the entire universe. It means a maximum lifetime of spatially restricted (evolutionarry) structures bound to ''l''<math>\,</math>* < ''R''H instead (while ''T'' ' = 0 means ''t'' * = –oo with respect to the universal time coordinate).

== Energy density and the negative gravitational pressure ==

The SUM component ''G''00 of the [[wikipedia:Tensor#Ko- und Kontravarianz|''covariant'']] [[wikipedia:Friedmann-Gleichung#Herleitung|Einstein-Tensor]] - obviously corresponding to the ''universal energy density'' - is temporally constant. On the other hand the [[wikipedia:Krummlinige Koordinaten#Tensoren zweiter Stufe|mixed co- contravariant]] component ''G''00, which would apply at application of [[wikipedia:Einsteinsche Feldgleichungen|gravitational equations]] on local [[wikipedia:Ideale Flüssigkeit|perfect fluids]], seems to depend on ''universal time'' ''t''<math>\,</math>*. But that such a dependence over arbitrarily large periods would be unrealistic again - opposed to locally restricted [[wikipedia:Zeitdilatation#Eigenzeit|proper times]] ''t'' - follows from the fact, that any special reference point of universal time ''t''<math>\,</math>* does not exist.
The SUM line element implies a negative gravitational pressure of –1/3 the ''[[wikipedia:kritische Dichte|critical density]]'' at each arbitrarily chosable zero point of universal time ''t''0* = 0. In contrast to ordinary particles in a box (which due to their positive pessure would immediately [[wikipedia:Diffusion|diffuse]] without its walls), galaxies within a limited region of the stationaty universe would mass together due to their mutual attraction if there was no negative gravitational pressure (caused by the gravitational potential of matter and energy outside).

== SUM result of two different values for the local and the universal Hubble constant ==

[[File:SNe-Ia-wiki.jpg|thumb|'''''Fig. W3 - Left panels (a)-(e)''''':
Comparing the SUM magnitude-redshift prediction (for <math>\kappa</math> = 0) with the SNe-Ia data and the CCM-prediction, there is a straightforward SUM agreement on large universal scales ''z'' > 0.1 where the universe may be rightly regarded homogeneous and isotropic. The red SUM-line coincides almost completely with the blue CCM-line (though of a 9 % higher Hubble constant).

-- '''''Intermediate right panel (b)''''': Full scale compatibility with the High-z Supernova Search Team's (HZT)
Riess et al. 'gold' data, if given a local Hubble contrast analogous to W2.

-- '''''Lower right panels (c),(d),(e)''''': Also in these panels again including the data of the Supernova Cosmology Project (SCP) as well, the
broken straight lines are determined by the method of least quadratic deviations and should ideally prove congruent with the respective z-axis.
]]

In both panels of Fig. W2 the solid blue lines may represent the real
SNe-Ia observations, the broken red lines respectively below do
represent straight SUM. A maximum deviation <math> \mathrm \delta z </math> ≈ 0.002 corresponds to a maximum Hubble contrast of ≈
+9%. With <math>H_{\mathrm{universal}}</math> ≈ 67 km/s/Mpc
e.g. this would mean <math>H_{\mathrm{local}}</math> ≈ 73
km/s/Mpc within <math> \mathrm{r^{\ast}}</math> < 110 Mpc, i.e. within <math>z</math> < 0.027 (while the mean value in the transition zone is about
<math>H_{\mathrm{trans}}</math> ≈ 70 km/s/Mpc).

Now recently there has been reported another "local value" <math>H_{\mathrm{0}}</math> = 73.2 km/s/Mpc with an uncertainty of only 2.4%
<ref>A.G. Riess et al., [http://iopscience.iop.org/article/10.3847/0004-637X/826/1/56/pdf "''A 2.4% Determination of the Local Value of the Hubble Constant''"], ApJ 826:56 (31pp), 2016, [[doi:10.3847/0004-637X/826/1/56]], [http://arxiv.org/abs/1604.01424 "arXiv:1604.01424"] </ref>
as well as 71.9 km/s/Mpc ±3.8% (approximately corresponding to 72.8 km/s/Mpc ±3.3% in Bonvin et al.
<ref>V. Bonvin et al., [http://adsabs.harvard.edu/abs/2017MNRAS.465.4914B "''H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: H0 to 3.8% precision from strong lensing in a flat ΛCDM model''"], [http://arxiv.org/abs/1607.01790 "arXiv:1607.01790]" </ref>.

Close to Freedman's value of 72 km/s/Mpc
<ref>W. L. Freedman et al., [http://iopscience.iop.org/article/10.1086/320638/meta/ "''Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant''"], ApJ, 553:47È72, 2001</ref>
, but in clear contrast to 67 km/s/Mpc predicted by the Lambda-CDM cosmology from the new Planck high-redshift measurements
<ref>N. Aghanim et al., [http://arxiv.org/abs/1605.02985 "''Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth''"], A&A 596, A107 (2016)</ref>
– or approximately also the 68 km/s/Mpc of Cheng Cheng & Qing-Guo Huang
<ref>Ch. Cheng and Q-G. Huang, [https://arxiv.org/abs/1409.6119 "''An accurate determination of the Hubble constant from baryon acoustic oscillation datasets''"], Sci China-Phys Mech Astron, 58 (2015), 599801 </ref>
– this remarkably means a Hubble contrast of about +9% again, the latter almost perfectly matching the original SUM prediction of 2007 in "Indication from the Supernovae Ia Data ..." {s. above as wll as also Fig. W2}. Apparently the authors of the new report
presuppose the 'curved' shape of a Lambda-CDM Hubble diagram (without
explicit justification) and therefore, of course, cannot find any difference between the local and global value of the Hubble constant.
This seems to be also the reason that the Hubble contrast previously
reported by Jha, Riess, & Kirshner
<ref>S. Jha, A.G. Riess, & R.P.Kirshner, [http://iopscience.iop.org/0004-637X/659/1/122/fulltext/ "''Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2''"], ApJ 659, 122-148, 2007 (s. a. weitere Literturangaben darin)</ref>
is no more discussed. There, however, it convincingly read: ''... the feature is present in the Hubble flow SN sample, and this has important implications for using SN Ia as tools for precision cosmology.''

Now the occurrence of two different values for the Hubble constant seems another unexpected coincidence between the contradictory Lambda-CDM framework and a consistent SUM concept. This proves that there may be
also other surprising features which are still to be found. The other
way round, with the clear SUM relations on hand it seems even possible to
determine the peculiar energy distribution in our probably anisotropic
'local' cosmic environment <math>z</math> < 0.1 with help of high precision
measurements of apparent SNeIa luminosities.

== Comparison with the Supernova-Ia data ==

To explain the Supernova-Ia data
<ref>A.G. Riess et al. (High-z Supernova Search Team),
[http://iopscience.iop.org/0004-637X/659/1/98/fulltext/ "''New Hubble
Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing
Constraints on the Early Behavior of Dark Energy''"], ApJ 659, 98-121,
2007</ref>
<ref>M. Kowalski et al. (The Supernova Cosmology
Project), [http://iopscience.iop.org/0004-637X/686/2/749/fulltext/
"''Improved Cosmological Constraints from New, Old, and Combined
Supernova Data Sets''"], ApJ 686, 749-778, 2008 </ref>
on sufficiently large universal scales the model SUM does not need any 'dark energy' and thus is also different from the [[wikipedia:Lambda-CDM-Modell|Lambda-CDM model]] as standard model of today's cosmology. Deviations in the region ''z'' < 0.1 are here reduced to a local Hubble contrast as in order of magnitude actually obseved. The universal SUM-[[wikipedia:Absolute Helligkeit|distsnce modulus]] results from the stationary line element as usual yielding
:<math>
(m-M)_\mathrm{SUM} = 5 \log{[(1+z) \ln{(1+z)}} + 25+ 5
\log{(\tfrac{R_\mathrm{H}} {\mathrm{Mpc}})}
</math>,
where the apparent [[wikipedia:Scheinbare Helligkeit|magnitude]] is represented by ''m'' and the [[wikipedia:Absolute Helligkeit|absolute brightnes]] of [[wikipedia:Supernova vom Typ Ia|Supernovae type Ia]] (SNe-Ia) as [[wikipedia:Standardkerze|''standard candles'']] by ''M''. The MG12 document ''Indication from the Supernovae Ia Data of a Stationary Background Universe''
<ref>P. Ostermann, http://www.icra.it/MG/mg12/talks/cot2_ostermann.pdf "''Indication …''"] MG12-Talk (please use the full-screen mode)</ref>
demonstrates the immediate agreement of SUM's distance modulus with the SNeIa data for universal scales ''z'' > 0.1 (if at all beyond such scales - in order of magnitude corresponding to that of the [[wikipedia:Sloan Great Wall|Sloan Great Wall]] - the universe can be rightly regarded to be homogeneous und isotropy).
There in a number of systematically successive illustrations it is shown why to overcome the expected predictions of the [[wikipedia:Friedmann-Modell#Einstein-de-Sitter-Modell|Einstein-de-Sitter model]] and that of the outdated [[wikipedia:Steady-state theory|Steady-state theory]] a strange concept of a 'dark energy' representing a fictitious [[wikipedia:cosmological constant|cosmological constant]] seemed necessary to explain the new observational data. Based on Einstein's original gravitational equations without such a constant of his "biggest blunder", however, the SUM line element had been immediately confirmed by the new Supernova measurements.
Even taking into account an infinite number of stars, due to [[wikipedia:redshift|redshift]] and [[wikipedia:time dilation|time dilation]] there results a realistic finite value for the low brightness (darkness) of the night sky. [[wikipedia:Heinrich Wilhelm Olbers#Olberssches Paradoxon|Olbers' paradox]] is solved here without any hypothesis concerning a 'big bang' or any spatial expansion.

== Alternative to a material contribution of 'dark energy' ==

In addition to the [[wikipedia:Inhomogenität|inhomogeneous]] contribution of indirectly meausurable dark matter there should be also a roughly homogeneously distributed transparent one, which in accordance with SUM is not even detectable by the effect of [[wikipedia:Gravitationslinseneffekt|gravitational lensing]]. This homogeneous part - in the [[wikipedia:Lambda-CDM model|Lambda-CDM framework]] ascribed to ''dark energy'' could fill the gap between that amount of the matter actually observed today and the [[wikipedia:Kritische Dichte|critical density]] required for a ''flat'' universe without spatial ''curvature''. At the same time there is no [[wikipedia:Expansion des Universums|expansion of space]] and therefore no need for any additional energy to accelerate the fictive universal expansion.

It is simply a wrong statement to read: ''"The measured <math>H_0</math> is also highly inconsistent with the simplest inhomogeneous matter models invoked to explain the apparent acceleration of the universe without dark energy"''
<ref>A.G. Riess et al., [http://iopscience.iop.org/0004-637X/730/2/119/fulltext/ "''A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3''"], ApJ 730, 1-18+1, 2011 ( Zusatztext )</ref>,
s. both panels b) of Fig. W3 on the left and on the right instead. That popular fallacy seems to rely on the erroneous presupposition of the fictive big-bang framework as a certain scenario. In fact this premature statement of Riess et al. 2011
is easily disproved. The refutation of that claim does not even
require any own special astrophysical expertise, since their publicly
available and Nobel awarded data seem rightly unimpeachable. Each ubuntu child may be able to debunk it as superstition (unfortunately almost soundig like a fake) by straighforwardly plotting the authors' own SNeIa 'gold' data in the
universal redshift range z > 0.1.


If, however, dark matter was built in parts of
thermalized neutrinos – as suggested by SUM and thereby possibly solving the most irritating 'dark energy' puzzle of modern cosmology – then it might be possible
to disprove the big-bang origin of the CMB directly by
identifying hDM particles emitting the CMB or
by detecting any such photons within shielded cavities
(today assumed instead to come from z > 1000). A preliminary
assessment would yield about
10 locally emitted hDM photons a year within a 1000-m<math>^3</math> tank (in rough order of magnitude; ideally such a
'surrounding detector' would have to be cooled down below
2.7 K). The unavoidable thermal radiation emitted from
any respective measuring device, however, might make a
clear classifcation of single photons most likely difficult
if not impossible in that frequency range.

== Microwave background radiation and a homogeneous part of 'dark matter' ==


[[File:rho_emiss.jpg|thumb|'''''Fig. W4''''' - The bold solid black line shows the total CMB spectrum for <math>\kappa</math> = 2 as actually observed. The bold broken red line shows the emission of the hDM radiation exemplarily in a local sphere of <math>\Delta r^*</math> = 100 Mpc as calculated. In addition, here the thin red solid lines show respective parts coming from within ''z'' = ''Z'' in this case ''from bottom to top'' by ''Z'' = 0.1, 0.2, .. 1.0 respectively.]]

In the famework of SUM the microwave background radiation (CMB) is explained in parts as thermal radiation of ''[[wikipedia:Dunkle Materie|'dark matter']]''. This concept may solve two fundameental problems at the same time: (a) there is no macroscopic distribution of matter without temperature or without thermal radiation; and (b) any stationary background radiation must have origined within the infinite universe.
In an initially purely mathematical derivation it has been possible, to compose a perfect [[wikipedia:Plancksches Strahlungsgesetz|Planck spectrum]] out of [[wikipedia:Rotverschiebung|redshifted]] radiation without the hypothesis of a 'big bang'.
At a statistically mean universal temperature the inhomogeneities of that cold ''[[wikipedia:Wärmestrahlung|thermal radiation]]'' seem to reflect the obviously existing [[wikipedia:Baryonische akustische Oszillation|acoustic oscillations]] of matter, which had formed also here over astronomical periods of time by the interplay of [[wikipedia:gravitation|gravitation]] and [[wikipedia:radiation pressure|radiation pressure]]. The chance alternatively to explain the CMB [[wikipedia:Anisotropie|anisotropies]] within SUM is obvious from the comparison of different illustrations as e.g. Figure 14-e of
''N. A. Sharp''<ref>N.A. Sharp, [http://articles.adsabs.harvard.edu/full/1986PASP...98..740S "''The whole-sky distribution of galaxies''"], Astr. Soc. Pacific (ISSN 0004-6280), vol. 98, Aug. 1986, p. 740-754, 1986</ref>
and Figure 7(b) of ''C. L. Bennett''<ref>C.L. Bennett et al., [http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/basic/wmap_cb1_images.cfm "''First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results''"], ApJS 148, 1, 2003</ref>
or Figure 5 of ''R. Piffaretti''
<ref>R. Piffaretti et al., [http://arxiv.org/pdf/1007.1916 "''The MCXC: a Meta-Catalogue of X-ray detected Clusters of galaxies''"], A&A, 534, A109, 2011</ref>.
In contrast to the concept of an etrenal infinite universe itself, the preliminary explanation of the [[wikipedia:Planck spectrum|Planck spectrum]] seems [[wikipedia:Falsifikationismus|falsifiable]] with help of the [[wikipedia:Sunjajew-Seldowitsch effect|Sunjajew-Seldowitsch effect]].

In any case it is no longer possible to take the sheer existence of the CMB as a certain proof for a big-bang origin of the entire universe.

== The alternative Sunyaev-Zel'dovich effect ==

[[File:Delta_rho.jpg|thumb|'''''Fig. W5''''' - The CMB parts
<math>\rho _Z^*</math> coming from ''behind'' <math>z = Z</math> according to SUM. Thin curved solid red lines are shown here
''from top to bottom'' for <math>Z</math> = 0.1, 0.2, ..
1.0.]]

The originnal effect of Rashid Sunyaev and Yakov Zel’dovich describes a slight distortion of the CMB background radiation by inverse Compton scttering of galaxy clusters. Different from the Cosmological Concordance Model (CCM) framework, according to its preliminary explanation in SUM that effect
<ref>R. Lieu, J.P.D. Mittaz, & S.-N. Zhang, [http://iopscience.iop.org/0004-637X/648/1/176/fulltext/ ''"The Sunyaev-Zel'dovich Effect in a Sample of 31 Clusters: A Comparison between the X-Ray Predicted and WMAP Observed Cosmic Microwave Background Temperature Decrement"''], ApJ 648, 176-199, 2006</ref><ref>L.E. Bleem et al., [http://arxiv.org/pdf/1409.0850 ''"Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey"''], ApJS, 216, 27, 2015</ref>
should be gradually weakened with increasing distances. At redshift ''z'' > <math>\,</math>1 it should approximately vanish except for statistical fluctuations. Remarkably the corresponding Planck-catalogues
<ref>P.A.R. Ade et al. (Planck Collaboration), [http://www.aanda.org/articles/aa/abs/2014/11/aa21521-13/aa21521-13.html "''Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts''"], A&A 571, A20, 2014 [http://arxiv.org/pdf/1303.5080, article PDF 2013]</ref><ref>P.A.R. Ade et al. (Planck Collaboration), [http://xxx.lanl.gov/pdf/1502.01597 "''Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts''", article PDF 2015]</ref>
do contain predominantly observations up to this limit.

Now in the statistics of the Sunyaev-Zel'dovich effect with the Planck 2015 data on hand, there has come a chance to decide whether or not the CMB once originated after a 'big bang', or whether, the other way round, the CMB is emitted from 'dark' matter within a non-expanding background universe.

[[File:SZE.jpg|thumb|'''''Fig. W6''''' - The realistic SZ effect
among other CMB distortions like e.g. re-shifting inhomogeneities. --
'''''Upper panel (a)''''':
Isothermal CMB fluctuations of order <math>y</math> ≈
10^{-4} are plotted in faint red, while the thin curved blue and grey
lines show changes of the local SZE.
-- '''''Bottom panel (b)''''':
This highly important Figure demonstrates a possibly resulting realistic SZ signal as bold red line (<math>X_{\mathrm{back}}</math> ≈ <math>-5 \cdot 10^{-5}</math>) where SUM's isolated
frequency shift according to the broken green line seems largely
compensated by such a random 'back'-ground inhomogeneity (lower
intensities might be understood as lower y's).]]

== Other observational facts and open questions ==
In addition to those observational facts of universal redshift and the apparent SNe-Ia magnitudes, which usually are claimed to be fundamental pillars of the [[wikipedia:Urknall|big bang theory]], but on the other hand most naturally to describe in the SUM framework, other important features seem to be alternatively explainable - though at least rudimentarily so far.

* Nucleosynthesis - In a stationary universe the respective parts of all material components is determined according to the laws of quantum mechanics by the requirement that in 'original processes' they be restored at the same rates as they have disappeared before in gravitational centers of extreme strength. The [[wikipedia:big bang|big bang]] model does presuppose in no place that outside a corresponding area of extreme temperature and density no other such events may happen (''multi bangs''). It even cannot be ruled out that the release of matter in form of [[wikipedia:jets|jets]] - incluasive plasma bubbles - provides a permanent restoration of [[wikipedia:Primordiale Nukleosynthese|primordial]] cores and her components.

* Quasar and older galaxy dstributions at great distances – Since in the years about 1960 it has been discovered, thet the [[wikipedia:quasar|quasar]] [[wikipedia:3C273|3C273]] was no nearby star, but at a redshift [[wikipedia:Rotverschiebung|Rotverschiebung]] of ''z'' = 0,158 in the region of distant galaxies, there have been later observed such bright [[wikipedia:quasi-stellar objects|quasi-stellar objects]] (QSOs) also in very much larger distances. In the meantime there have been discovered quasars up to redshifts of at least ''z'' = 7,1. It follows, that the nearest of them may be located today in cosmic neighborhood. Even a final conclusion that QSOs are only at distances above average would be selfunderstood, if the evolution of our 'local' cosmos had started from a ''multi bang'' event (compatible with SUM). This could also be a reason that most distant galaxies may look younger. On the other hand the measured frequency scale of quasars seems to be at first reduced (and then limited) at large scales ''z'' > 2-3 by [[wikipedia:Selbstselektion|effects of self selection]] like the so-called ''[[wikipedia:Gunnar Malmquist|Malmquist bias]]'', while all objects below a weak brightness limit remain unconsidered.

* Principal SUM differences from a 'big bang' origin out of nothing – Tough various fundamental observationall facts known as 'pillars' of [[wikipedia:Urknall|big bang cosmology]] seeem numerically to be brillantly confirmed, there actuallly remain several important questions. A ''[[wikipedia:Vakuumenergie|false vacuum]]'' of ''[[wikipedia:Vakuumfluktuation|quantum fluctuations]]''<ref>V.F. Mukhanov & G.V. Chibisov, [http://arxiv.org/pdf/astro-ph/0303077 "''Quantum fluctuations and a nonsingular Universe''"] (re-print), 1–8, 1981</ref> could not exist without an energy density, if our evolutionary cosmos had originated according the [[wikipedia:Urknall|big bang theory]] out of that an essence. Even such a ''[[wikipedia:Tohuwabohu|tohu-va-bohu]]'' would require a physical description as a ''[[wikipedia:Urknall#chaotische Inflation|chaotic background]]'' by [[wikipedia:Albert Einstein|Einstein's]] [[wikipedia:Einsteinsche Feldgleichungen|graviational equations]]. Except of the SUM framework no such solution seemms to exist. Indeed here do not arise any correspondihg questions of the Lambda-CDM Concordance Cosmology or they appeear in completely different light.

* Restriction of the law of entropy to evolutionary processes - At gravitational processes of new recreation, possibly in super massive objects like [[wikipedia:active Galaxienkern|active galaxy nuclei (AGNs)]], [[wikipedia:Hypernova|hypernovae]] or sources of [[wikipedia:Gammablitz|gamma-ray bursts]], the entropy has to temporarily decrease in local areas of an eternal universe to remain stationary in total. To this effect it requires a restriction of the law of permanent increase of [[wikipedia:Entropie#Zweiter Hauptsatz|entropy]], without a risc to contradict any experimental experience made by living beings ever. The equirement of a temporarily local restriction of entropy is inevitably necessary for every stationary concept at all (otherwise there would arise that strange ''[[wikipedia:Wärmetod (Physik)|heat-death of the universe]]'' as already discussed long ago). Even if such a restriction may sound improbable, however, it is less improbable than an origin of the entire universe from this ''[[wikipedia:inflation (cosmology)#emergence from nothing?| nothing]]''.

To overcome fundamental ''fine tuning'' problems of the [[wikipedia:Urknall|big bang theory]], which are related to ''spatial flatness'' of the universe, the non-existence of ''magnetic monopoles'' or its fictive ''horizon'', there has been invented a phase of ''[[wikipedia:Inflation (Kosmologie)|cosmic inflation]]''. This should have been driven by a scalar ''[[wikipedia:Inflation (Kosmologie)#Felddynamik|inflaton field]]'', which never has been observed, though. Also the fact of the universal ''[[wikipedia:matter-antimatter asymmetry|matter-antimatter asymmetry]]'' is significantly incompatible to experiental experience in today's predominant framework of the current Cosmologial Concordance Cosmology. Just as little it is understood from the original [[wikipedia:Urknall|big bang theory]], that after a unversal origin from nothing there could be consistent steady laws of nature at all (and not all ''events'' do happen only chaotically to this day). Irritating is also an appeal to an imperfect [[wikipedia:cosmological principle|cosmological principle]] arbitrarily excluding only ''time'' from the otherwise pefect universal symmetry. The biggest of all appears in the coincidence that the span of time ''t''0 usually called ''age of te universe'' should approximately only today equal the reciprocal value of the conventional [[wikipedia:Hubble parameter|Hubble parameter]] 1/''H''0.

According to SUM the ''[[wikipedia:Anthropisches Prinzip|anthropic prinziple]]'' does not only apply to the stationary universe itself, but to all local evolutionary cosmoses possibly therein. By the adjustment of the [[wikipedia:big bang|big bang]] concept having been extended in the meantime - from originally only one ''big bang'' universe via additional ''[[wikipedia:parallel universes|parallel universes]]'' up to one [[wikipedia:multiverse|multiverse]] now all-embracing again - cosmology finally seems fürther to develop to the SUM concept with his natural distinction of the stationary universe from evolutionary ''multi bang'' or local ''quasi bang'' cosmoses. In the context of the alleged universal age and assumed boundaries it has to be remarked that corresponding ideas have been extended again and again, since [[wikipedia:Immanuel Kant|Immanuel Kant]] recognized in star nebulae, even observable at those times, possible other ''Milky Ways''.

== The reconcilableness of relativity theory (RT) and quantum mechanics (QM) ==

Six years after the intermediate completion of [[wikipedia:Allgemeine Relativitätstheorie|general relativity]] (GR) [[wikipedia:Albert Einstein|Albert Einstein]] has confronted in ''Geometrie und Erfahrung''
<ref>A. Einstein, [http://einsteinpapers.press.princeton.edu/vol7-doc/431 "''Geometrie und Erfahrung''"] (erweiterte Fassung des Festvortrags), Julius Springer, Berlin 1921</ref>
two mathematically possible interpretations and thereby explicitly admitted [[wikipedia:Henri Poincaré|Poincaré]]'s claim of understanding the [[wikipedia:Nichteuklidische Geometrie|non-euclidean geometry|]]
<ref>H. Poincaré, [https://archive.org/details/wissenschaftundh00poin/"''Wissenschaft und Hypothese''"], autor. dt. Ausg. von F. und L. Lindemann , Teubner 1904 (Das Original “La Science et l’Hypothèse” wurde vor 1905 von Einstein gelesen und, wie von seinem Freund Maurice Solovine in der 'Akademie Olympia' wochenlang diskutiert).</ref>
("''Sub specie aeterni in my opinion Poincaré is right with this interpetation''"). Therefore it is possible to ascribe the non-euclidean geometry of GR not to space and time itself, but to gravitationally affectable unit sticks, clocks, and to all other real physical objects
and otherwise to keep [[wikipedia: euclidean geometry|euclidean geometry]] for the one complete description of all natural event. This turns out to work with the help of [[wikipedia:Nathan Rosen|Nathan Rosen]]'s ''bi-metric relativity''
<ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]].</ref>.
On the other hand such a chance would even explain why in spite of big efforts like in ([[wikipedia:string theory|string theory]], [[wikipedia:loop quantum gravity|loop quantum gravity]]) no concept seems to have convincingly succeeded to quantize ''[[wikipedia:spacetime|spacetime]]'' and thus to basically reconcile the conventional relativity theory with quantum mechanics in a [[wikipedia:allgemeine Relativitätstheorie#Quantenphysik|unified theory of gravitation and quantum mechanics]]. According to SUM, however, seems possible as a matter of principle to allow valid statements in future to otherwise mere mathematical ''[[wikipedia:Singularität (Astronomie)|singularities]] of GR or at least protect from misinterpretations. Besides the ''[[wikipedia:allgemeine Relativitätstheorie#Schwarze Löcher|back holes]]'' this also concerns the [[wikipedia:Singularitäten-Theorem|singularity theorems]] von [[wikipedia:Stephen Hawking|Hawking]] und [[wikipedia:Roger Penrose|Penrose]], where in the absence of a consistent unified theory the detailed quantum structure of matter had to be neglected so far.

== Numerical hints to the existence of 24 elementary spin-1/2 torsion particles ==

Though of unprecedented numerical success in describing the observational facts of modern cosmology, there is another strange hint that the inflationary Lambda-CDM big-bang model might fail. This is because of an apparent materialization of an antisymmetric torsion tensor <math>T_{ikl}</math>.
The universe seems constituted of 24 elementary spin-½ particles which are 6 leptons + 3 colors * 6 quarks. These curling structures, behaving as 'whirl' particles, may represent exactly the 24 components of a real torsion tensor which naturally include 6 'temporal' + 3 * 6 'spatial' constituents

<math>T^i_{kl}</math> =
<math>T^0_{\alpha\beta}+T^\gamma_{\alpha\beta}</math>,

what seems to be more than a mere coincidence [here Latin indices ''i'', ''k'', ''l'' ... = 0, 1, 2, 3 in contrast to Greek spatial indices, here <math>\gamma</math>, <math>\alpha</math>, <math>\beta</math> ... = 1, 2, 3 only].
In addition, of the 6 'lepton'-components in <math>T_{\alpha \beta}^0</math> there may be 3 'electric' + 3 'magnetic' (according to the assignment in the electromagnetic field strength tensor), thus reflecting three <math>e, \mu, \tau</math> particles plus three respective <math>\nu _e, \nu _\mu, \nu _\tau</math> neutrinos. As has been shown by Landau & Lifshitz
<ref>L.D. Landau & E.M. Lifschitz: Klassische Feldtheorie; Lehrbuch d. theor. Physik, Bd. II, 12. Aufl., Berlin 1992</ref>
long time ago, however, the physical existence of a non vanishing torsion tensor would contradict Einstein's equivalence principle. This principle is underlying the literally geometric interpretation of his gravitational equations, while in view of SUM the geometric approach fails in reducing physics to exclusively Riemannian properties of non-Euclidean space and time as also indicated by the existence of tetrads
<ref>P. Ostermann, "''[http://independent-research.org/assets/tetrad13.pdf A natural vierbein approach to Einstein’s non-Euclidean line element in view of Ehrenfest’s paradox]''"; 2013</ref>.
Therefore not only a microscopic violation of the fundamental equivalence principle would contradict the whole spacetime concept where today's Concordance(Consensus) Model of cosmology is relying on. In view of extended elementary spin-½ torsion structures (in most situations identifiable and acting as wholes) also Heisenberg's uncertainty principle can be understood in contrast to the strange behavior of 'point' particles otherwise unrealistically presupposed so far. In any case, contrary to its historical reception, quantum mechanics may be understood as theory of extended whirl structures of variable shape (i.e. as theory of possible 'torsion particles'). A first deductive attempt to extended structures (outlined by
<ref>P. Ostermann, "''[http://independent-research.org/assets/06b.pdf Skizze einer offenen Theorie von Elektrodynamik, Gravitation, Quantenmechanik]''"; 2006</ref>.<ref>P. Ostermann, "''[http://independent-research.org/assets/08.pdf Basic relations of a unified theory of electrodynamics, quantum mechanics, and gravitation]''"; MG11 Proceedings 2008</ref>
seems to explain Bohr's energy-frequency formula and to imply Heisenberg's uncertainty relations in accordance with approved principles of relativistic physics. Thus this feature is shown to be anything but an incomprehensible surprise after all.

Particles like electrons and protons as well as their constituents are neither real mass points without any extensions nor one-dimensional 'strings', nor two or higher-dimensional 'branes', but they are three-dimensional deformable structures with particle parameters in form of several characteristic constant integrals pertaining to rest mass, charge, and spin among others. This concept, though, does not deny fundamental achievements of mathematical abstractions (like in particular the concept of 'point masses' in Newtonian mechanics), of course.
Also the quantum mechanical result that particles do not have an unambiguous momentum is only a natural statement in view of interacting extended structures, where a possibly varying momentum ''density'' is self-evident. On the other hand, in spite of unavoidable
uncertainties due to relative inner motions, the total momentum of a free particle can be exactly determined. While inner details may prove strange, the natural laws behind should be clear. In contrast to solid bodies, remarkable characteristics of torsion structures are a completely different steadiness and their temporally dissolved identities. It is obvious that a theory of elementary whirl particles subdivides kinematics and dynamics of existing structures from a theory of production and transformation ('Erzeugung und Verwandlung' in Einstein's words). Contrary to naive point-particle models, the new concept allows a fundamentally simple understanding of transformations. While concerning free motion of whole objects, only kinematics may be of interest, in particle physics inner forces play the decisive role. Even the indistinguishability of elementary particles of same kind – otherwise a complete mystery – is no longer unintelligible as well as interference and diffraction phenomena.

The torsion model is independent of the question whether such particles may exist as material objects in vacuum or in form of whirl structures in a continuously extended medium. Nature may show both aspects (like spiral nebulae in a background of dark matter, for example). It seems an evident chance that:
 
– Elementary particles are whirl structures. 
– Due to the conservation law of angular momentum the tiny extended free torsion structures are in parts steady for cosmologcal periods of time. 
– Torsion particles are subject to processes of formation and decay. 
– In transitional phases whirl structures lose their identity. 
– On one hand torsion structures may be approximately described as particles. 
– In other situations torsion structures may be approximately described as waves. 
– Detailled velocities of parts of torsion structures are realized at the same time as the motion of their respective center of gravity. Natural relations of uncertainty follow from that.
 
Thus the elementary particles, which are assumed to constitute the entire universe, are essentially different from those eternal solid 'atoms' of the pioneering antique philosophers Leucippus and Democritus. Since it is clear that only at the price of unavoidable uncertainties
torsion structures can be dealt with as extensionless point particles, a complete relativistic mechanics has to contain a future consistent
formulation of quantum theory. As already addressed in SUM14, an appropriate basis will be Rosen's bi-metric relativity
<ref>N. Rosen, "''General Relativity and Flat Space I/II''", Physic. Rev. 57, 147-153, 1940, [[doi:10.1016/0003-4916(63)90293-8]]</ref><ref>N. Rosen, "''Flat-Space Metric in General Relativity Theory''", Ann. of Physics 22, 1–11, 1963, [[doi:10.1016/0003-4916(63)90293-8]]</ref>
after fixation to the (preferred) universal frame.

== History, SUM precursors, various related attempts ==

It is impossible to do cosmology without appropriate principles which – besides the indispensable compatibility to observational facts – should fulfill the criteria of simplicity, adequacy and clarity. In the absence of such criteria not even the decision between a heliocentric and a geocentric conception of our planetary system would be possible within GR because of legitimate mutual coordinate transformations.

Albert Einstein establishing relativistic cosmology has started from the presupposition of an eternal universe
<ref>A. Einstein, "''[http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1917SPAW.......142E&link_type=ARTICLE Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie]''", Sitz. Preuß. Akad. Wiss., 142-152, 1917</ref>.
Hiis attempt failed because he had searched a purely ''static'' solution, whose line element - as opposed to that of [[wikipedia:Alexander Alexandrowitsch Friedmann|Friedmann]] as well as to about a hundred years later now to the line element of the stationary solution SUM - does not contain in the corresponding gravitational potentials ''gik'' any coordinate of time. This also applies to the original form of [[wikipedia:De-Sitter|De-Sitter]]'s model, which however allowed a transfer into the later Steady-state Theory by a mere coordinate transformation.

* Steady-state Theory: Under the name [[wikipedia:Steady State Theory|Steady State Theory]], which tried to describe a steady expansion, in the year 1948 a model was presented (due to differing observational facts later failed in various versions) which in view of its authors because of permanent new creation of matter from nothing - in clear contrast to SUM - should have been regarded to be filled with constant matter density. Only recently it became known that already Einstein essentially anticipated and rejected the concept of this theory. A new ''C'' field introduced by [[wikipedia:Fred Hoyle|Fred Hoyle]] may be regarded as precursor of the scalar field of today's inflationary Lambda-CDM model. In spite of its name [[wikipedia:Steady-state Theory|Steady-state Theory]] the redshift values of individual galaxies do not result steady as constants (except of their peculiar motions), but corresponding to the titles of those articles (explicitly refering to an ''expanding universe'') would continuously increase.

* Coasting Cosmology: A model of a more general form of the linee element than that of SUM shown above - but including a [[wikipedia:scale factor|scale factor]] ''HT'' - has been discussed at its time as a universe of ''coasting'' expansion <ref>E.W. Kolb, [http://adsabs.harvard.edu/full/1989ApJ...344..543K "''A coasting cosmology''"], ApJ 344, 543-550, 1989</ref>, before in the year 2011 a closely related concept has been discussed once more in the context of today's big bang Lambda-CDM cosmology <ref>F. Melia F. & A.S.H. Shevchuk, [http://arxiv.org/pdf/1109.5189 "''The Rh = ct Universe''"], MNRAS 419, 2579, 2012</ref>. Both models are on principle different from SUM (the fundamental consequence of constant values of redshift from sources in constant universal distances was originally not even mentioned there).

* Chaotic Inflation: The physicist [[wikipedia:Andrei Dmitrijewitsch Linde|Andrei Linde]] has developed the concept of [[wikipedia:Urknall#chaotische Inflation|chaotic inflation]]<ref>A. Linde, "''Chaotic Inflation''", Phys.Lett. 129B, 177–181, 1983</ref><ref>A. Linde, [http://iopscience.iop.org/1402-4896/2005/T117/005/pdf/1402-4896_2005_T117_005.pdf "''Prospects of Inflation''"], Phys. Scripta T117, 40–48, 2005</ref> and thereby overcame the theoretical fixation on one single big bang from nothing. On the other hand there is dealt with ''parallel'' universes, where each of them had origined with own inflation and even possibly own laws of nature. This clearly contradits SUM's fundamental presupposition of many cosmic areas within one universe of everywhere the same laws of nature (multiverse). In that context - though of completely different mathematics - also appeared a title 'Stationary Universe Model'<ref>A. Mezhlumian, [http://arxiv.org/pdf/astro-ph/9410039 "''Stationary Universe Model: Inputs and Outputs''"], Stanford Pre-print, 1–11, 1994</ref> for the first time. With regard to a universe eternally situated in change there obviously always had been corresspondig ideas, which seem related to [[wikipedia:Samsara|cycle of growth and decay]] in eastern religions.

Also in view of [[wikipedia:Epikur|Epikur]] there exist an infinite number of worlds in infinite large space, what has ben reported by Lucretius in ''[[wikipedia:De rerum natura|On the Nature of Things]]''. According to [[wikipedia:Rhazes|Rhazes]] - in sense of timeless laws of nature - there shall be an eternal matter from atoms, an absolute and eternal universal time (different from relative 'proper' time) as well as an absolute and eternal space being unchanging. Similar concepts of space and time are found later from Newton. [[wikipedia:Nikolaus von Kues|Nikolaus von Kues]] has thought about a [[wikipedia:Parallelwelt|multiplicity of worlds]] in a single infinite universe. The according to modern natural science revitalized idea of an eternal infinite universe, however, is existing at the latest since [[wikipedia:Thomas Digges|Thomas Digges]]. His contemporary [[wikipedia:Giordano Bruno|Giordano Bruno]] defended the idea of "many worlds ", what is shown in particular from his document of 1584 ''About the infinite, the universe and the worlds'' (choice of words of this title corresponds also to SUM's distintion of "Universe" from " cosmoses"). He had the idea that this [[wikipedia:Giordano Bruno#Unendlichkeit des Weltalls|eternal infinite universe]] was interwoven by the same divine pulse. His thinking had become influenced by the predecessors mentioned above. In the context of SUM it has now been shown that corresponding concepts are not only compatible to Einstein's equations, but seem to follow from them. On the one hand, although this new model is hardly realized till now by mainstream-cosmology, but on the other hand the current ''Cosmological Concordane Model'' (CCM) including its highly speculative ''[[wikipedia:phase of inflation|phase of inflation]]'' (founded by no experimental experience but indispensable there) seems to strike increasing scepticism with quite a few people.

The idea leading to SUM, which is shown to be the only arguable solution of Einstein's original equations without cosmological constant, is that no universal horizons must limit physical reality. Beyond local applicability any 'proper' SRT concepts will prove overstrained in the conventional GRT framework. Therefore SUM demands a scientific discussion instead of an endless sham fight against the outdated historical attempt of the SST. In contrast to apparent attempts based on premature fictions of a big bang and accelerated expansion of space it is a matter of course that ubuntu cosmology is not to teach nature, but to learn from and to describe the universe in awe and with due modesty.


== Literatur ==
* Peter Ostermann, "''SUM – Model of a Stationary Background Universe Behind Our Cosmos''", digIT Verlag, 2014, ISBN 978-3-941550-25-4.
* Steven Weinberg, "''Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity''", Wiley, New York 1972, ISBN 0471925675.
* Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar, "''A Different Approach to Cosmology''", Cambridge University Press, 2000, ISBN 0-521-66223-0.
* Collected Papers of Albert Einstein (CPAE) – ''[http://www.einstein-website.de/z_information/papersproject.html Einstein Papers Project]''

== Einzelnachweise ==
<references />

[[wikipedia::Kategorie: Kosmologie (Physik)]] - 14. August 2018 - ENGLISH

File:Delta rho.jpg

2026-02-14T13:11:33Z

Admin:

File:Hubble-contrast.jpg

2026-02-14T13:11:28Z

Admin:

File:Rho emiss.jpg

2026-02-14T13:11:22Z

Admin:

File:Rho emiss local.jpg

2026-02-14T13:11:16Z

Admin:

File:SNe-Ia-start.jpg

2026-02-14T13:11:10Z

Admin:

File:SNe-Ia-wiki.jpg

2026-02-14T13:11:04Z

Admin:

File:SUM scale factor.jpg

2026-02-14T13:10:55Z

Admin:

File:SZE.jpg

2026-02-14T13:10:35Z

Admin: