General
Relativistic Cosmology| General
Relativistic Cosmology |
In General > s.a. cosmology; singularities.
* Precursor: See E A
Poe's 1849 "Eureka" (bb with periodic
universe).
* Result: It is a consequence
of the singularity theorems that, if general relativity is correct, a couple
of reasonable assumptions are satisfied, and there
is as much matter as we see, there must have been a big bang.
> Models: see modern
cosmological models and general relativistic
models.
Averaging / Smoothing of Inhomogeneities (Fitting Problem) > s.a. observational
cosmology; cosmological perturbations [back-reaction].
* Idea: Any explicit
averaging scheme of the type essential for describing the large-scale behaviour
of the universe yields corrections to the Einstein equation applied in the
cosmological setting; 2007, The question of whether or not these corrections
are significant is still a subject of debate, partly due to possible ambiguities
in the averaging schemes available, but Paranjape & Singh have shown that
not all effects are gauge.
* Approaches: Buchert & Carfora
summarize the effects that quantify the difference between "bare'' and "dressed''
parameters as "curvature backreaction''
and "volume effect''; The "macroscopic gravity" approach modifies
the Einstein field equation on cosmological scales by appropriate gravitational
correlation terms, that in a homogeneous, isotropic model have the effect of
an extra curvature.
@ General references: Carfora & Marzuoli PRL(84);
Hemmerich A&A(87);
Ellis & Stoeger
CQG(87);
Hellaby GRG(88);
Zalaletdinov GRG(92),
BASI(97)gq;
Zotov & Stoeger
CQG(92);
Futamase PRD(96);
Buchert ap/97-in;
Linder ap/98 [and
observation]; Boersma PRD(98)gq/97;
Stoeger et al IJMPD(07)gq/99 [linearized];
Sicka et al ap/99-in;
Tanimoto gq/99,
PTP(99)gq [model];
Buchert & Carfora PRL(03)gq/02 [and
scaling]; Ellis & Buchert PLA(05)gq
[rev, and entropy]; Zalaletdinov gq/07-in,
IJMPA(08)-a0801-in
[and macroscopic gravity]; Paranjape & Singh PRD(07)gq,
GRG(08),
Paranjape IJMPD(08)-a0705-GRF
[corrections to Friedmann equations]; Célérier a0706-in;
Mattsson & Ronkainen JCAP(08)
[scale dependence]; Reiris CQG(08)
[k = –1 Friedmann-Lemaître]; Larena PRD(09)-a0902 [for
a tilted set of observers]; Paranjape a0906-PhD.
@ And Ricci flow:
Piotrkowska gq/95-in;
Buchert & Carfora CQG(02)gq;
Carfora & Buchert in(08)-a0801;
> s.a. riemannian geometry.
@ And evolution, acceleration:
Buchert et al PRD(00)ap/99 [back-reaction];
Seriu CQG(01)gq;
Buchert CQG(06)gq/05 [globally
static without cosmological consant], CQG(05)
[effective equation of state]; Gruzinov et al JCAP(06)ap [heuristic
model, effects
O[H2l2/c2];
Paranjape & Singh GRG(08)-ap/06,
PRL(08)-a0806,
Sussman
a0807 [no significant
effect]; Li et al FdP(08)-a0801-in;
Buchert & Carfora CQG(08)-a0803;
Brown et al JCAP(09)-a0811;
Coley a0812 [in
terms of paths of photons]; Anastopoulos PRD(09)
[back-reaction].
@ Types of spacetimes: Coley & Pelavas PRD(06)ap,
PRD(07)gq/06 [spherical
symmetry]; Barrow & Tsagas CQG(07)gq/06 [anisotropic].
@ Techniques: Seriu GRG(00)gq [spectral];
Seto ApJ(00)ap [perturbative];
Buchert & Carfora in(02)gq/01
[geometry of scaling]; Buchert GRG(01)gq [effective
equation of state]; Coley et al PRL(05)gq,
van den Hoogen JMP(09) ["macroscopic
gravity"]; Behrend PhD(08)-a0812;
Coley a0908 [in
terms of scalar curvature invariants].
@ In Newtonian cosmology: Buchert & Ehlers A&A(97)ap/95;
Buchert ap/95-in,
GRG(00)ap.
@ Effects: Russ et al PRD(97)
[age]; Buchert & Carfora ap/03-in;
Coley
a0704 [and observational
cosmology]; Wiltshire PRL(07)-a0709
[and acceleration]; Khosravi et al IJMPD(09)-a0709 [dark-matter-like
behavior]; > s.a. acceleration, expansion,
friedmann equation.
Other Concepts and Effects > s.a. collapse;
schwarzschild spacetime; test-body
orbits; thermodynamics; time.
* Isolated objects in cosmological
backgrounds:
The main models available are the Einstein-Straus ("swiss cheese")
and McVittie ones; There is no known exact solution that smoothly interpolates
between a
black hole and an expanding universe.
@ Local particle dynamics: Anderson PRL(95);
Bonnor
MNRAS(96); Cooperstock et al ApJ(98)ap;
Mashhoon et al CQG(07).
@ Other local matter: Bonnor
CQG(99)
[H atom]; Matravers & Humphreys GRG(01)gq/00 [Einstein-de Sitter,
collapsing dust]; > s.a. gravitating
matter; lensing [models]; Thomson
Scattering.
@ Einstein-Straus model: Einstein & Straus RMP(45);
Mars PRD(98)gq/02 [axisymmetric],
CQG(01);
Mena et al PRD(02)
[anisotropic]; Grenon & Lake a0910 [generalized].
@ Local effects: Bonnor GRG(00);
Bolen et al CQG(01)gq/00 [precession
in McVittie spacetime]; Miller & Rouet ap/01 [on
structure]; Domínguez & Gaite EPL(01)ap;
Aurell & Fanelli
cm/01 [evolution
of perturbations]; Ellis NAR(02);
Bel gq/03 ["osculating
spacetime"]; Mizony & Lachièze-Rey A&A(05)gq/04;
Mashhoon et al CQG(07)-a0705;
Carrera & Giulini a0810; > s.a. schwarzschild [McVittie].
@ Other effects on gravitating objects: Dumin ap/02/A&A, Dvali et
al PRD(03)hp/02 [Moon
orbit].
@ And gravitational waves: Abramo PRD(99)ap [energy
density and p]; Creighton gq/99.
@ Isotropization: Lim et al PRD(04)gq/03;
> s.a. bianchi models, type
I, type IX and other
types.
@ And entropy, thermodynamics: Barrow NA(99)ap;
Valageas & Silk A&A(99)ap;
Brustein PRL(00)gq/99;
Moreschi gq/99.
@ Structural stability, fragility:
Tavakol & Ellis PLA(88); Coley & Tavakol GRG(92).
@ Related topics: Barrow gq/97-in,
Barrow & Maartens
PRD(99)
[anisotropic stress]; Jones gq/02/AN
[and quantum cosmology]; Ringström CMP(06)
[future decay of curvature].
> Issues and effects:
see cosmological
geometry and topology, observations,
perturbations; early-universe
cosmology.
> Concepts and techniques:
see gödel [rotation];
gravitational thermodynamics; renormalization.
With Varying Constants > s.a. variation
of constants; [branes, Metric-Affine
Gravity, scalar-tensor theories, supergravity,
other theories].
* Motivation: A scale dependence of G and 
is
given by the flow equation of the effective action for gravity.
@ Varying c: Albrecht & Magueijo PRD(99)ap/98;
Barrow ap/98;
Coule MPLA(99)gq/98;
Bassett et al PRD(00)ap;
Magueijo PRD(00)gq;
Chimento & Jakubi
IJMPD(01)
[pfluids]; Alexander & Magueijo ht/01 [non-commutative
geometry]; Niemeyer PRD(02)ap/01 [stringy
cutoff]; Moffat IJMPD(03)ht/02,
IJMPA(05)gq/04-in
[bimetric]; Youm PRD(02)ht [and
second law of thermodynamics]; Barrow PLB(03)gq/02;
Szydlowski & Krawiec PRD(03)gq/02 [dynamical
systems]; Chakraborty et al PS(03)
[with fluid]; Kragh SHPMP(06)
[historical]; > s.a. cosmological
constant.
@ Varying G: Barrow & Parsons PRD(97); Barrow et al PLB(02)gq [and 
].
@ Varying G and cosmological constant:
Abdel Rahman NCB(00); Bonanno & Reuter
PRD(02)
[from renormalization]; Singh IJTP(06),
MPLA(06)
[k = 0 FRW model + pfluid]; Bonanno et al CQG(07)gq/06 [Noether
symmetry approach].
@ Varying : Barrow & Mota
CQG(02)gq; Barrow et al PRD(02)ap/01; Mota & Barrow PLB(04).
@ Related topics: Belinchón IJTP(00);
Sandvik et al PRL(02)ap/01 [e or ];
Barrow
et al CQG(04)ap [and
bounces].
References > s.a. history
of relativistic physics; physics [Higgledy-Piggledy,
etc].
@ Books, I: Sciama 71; Kaufmann 77; Weinberg 77; Preston 87; Parker 88; Trefil
88; Barrow 94; Rees 96.
@ Texts: Eddington 33; Schrödinger 56; Bondi 68; Ryan 72; Zel'dovich & Novikov
75; Walker 76; Landsberg & Evans
77; Heidmann 80; Raychaudhuri 80; Novikov; Narlikar 88; Berry 89; Dolgov et
al 90; Islam
92; Raychaudhuri et al 92; Lachièze-Rey 95 [II]; Rowan-Robinson
96; Hoyng 06 [II; r CQG(07)].
@ Texts, III: Peebles 71; Weinberg 72; Börner 93; Peebles
93.
@ Reviews:
Freedman SA(92)nov; Steinhardt ap/95;
Matarrese ap/96-in;
Peebles ap/98-in,
PASP(99)ap/98;
Ellis & van Elst in(99)gq/98; Magueijo & Baskerville
PTRS(99)ap;
Ellis GRG(00)
[status]; Cotsakis gq/01-in;
Rebouças gq/02-in.
@ Texts, mathematical: Heller 94; Wainwright & Ellis ed-97.
@ Reviews, emphasis on inflation: Ellis in(91); Kamionkowski Sci(98)ap;
Turner ap/99-in;
> s.a. inflation.
@ General references: Milne 51 [dR < c dt];
Bergmann FP(70);
Ellis in(71); Ellis & Sciama in(72)*; Sachs in(73); MacCallum
in(75); Olivo-Melchiorri & Melchiorri RNC(85);
Ford GRG(87)
[
< 1 and future
expansion];
Jantzen PLB(87)gq/03;
Lidsey GRG(93)
[fragility and rigidity]; Chiba & Takahashi ap/07/PRD
[consistency relation, vs other theories].
@ Philosophical: Torretti in(79).
@ Challenge to big bang: MNRAS 239(89)201
[comment Maddox Nat(89)aug];
Narlikar
NS(91)mar.
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oct 2009