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; 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.
@ Smoothing: 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].
@ Smoothing, Ricci flow: Piotrkowska gq/95-in; Buchert & Carfora CQG(02)gq; Carfora & Buchert a0801-in; > 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 ap/06 [heuristic model, effects O[H2l2/c2]; Paranjape & Singh ap/06-GRG, a0806, Sussman a0807 [no significant effect]; Li et al a0801-in; Buchert & Carfora CQG-a0803.
@ 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 gq/01-in [geometry of scaling]; Buchert GRG(01)gq [effective equation of state]; Coley et al PRL(05)gq ["macroscopic gravity"].
@ 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 a0709 [dark-matter-like behavior]; > s.a. acceleration, expansion, friedmann.

Other Concepts and Effects > s.a. collapse; schwarzschild; 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 [EdS, 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].
@ 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 st"]; Mizony & Lachièze-Rey A&A(05)gq/04; Mashhoon et al a0705; > 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.
> Concepts and techniques: see gödel [rotation]; gravitational thermodynamics; renormalization.

With Varying Constants > s.a. variation of constants; [branes, Metric-Affine, scalar-tensor, 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 + 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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