Cosmological Models in General Relativity  

In General > s.a. 3D general relativity; early universe [including bounces, cyclic]; gravitation; string phenomenology; supergravity.
* Idea: Based on what we see observationally, we need models which are statistically homogeneous and isotropic on large scales.
@ Isotropic: Starobinsky PLB(80); Miritzis et al G&C(00) [Painlevé integrability].
@ G2: van Elst et al CQG(02); Carot & Collinge CQG(03) [scalar field, as dynamical system]; Fernández & González JMP(04) [stiffluid].
@ Closed models: Lasenby & Doran PRD(05)ap/03 [with inflation]; Heinzle et al PRD(05)gq/04 [Bianchi IX and Kantowski-Sachs pfluid].
@ Classification, overviews: Fischer GRG(96); Coley gq/99-proc, Wainwright & Lim JHDE(05)gq/04 [dynamical systems]; Barrow PRD(14) [4(1+F)+2S independent functions]; Leon & Fadragas a1412-book [dynamical systems].
@ Other models: Hayward & Twamley PLA(90) [spatially compact hyperbolic]; Rendall gq/94 [locally homogeneous]; Gott & Li PRD(98)ap/97 [self-generating]; Ellis & van Elst in(99)gq/98 [covariant 3+1]; van Elst et al PRD(00)gq [discontinuous]; > s.a. models in cosmology; solutions with matter.
@ Related topics: Tsamis & Woodard PLB(98) [expansion rate]; Krauss & Turner GRG(99)ap [future]; > s.a. generalized cosmologies.

Homogeneous and Isotropic > s.a. cosmological principle; observational cosmology; friedmann equation; FLRW models; Milne Universe.
* Standard model: It is based on the cosmological principle, and predicts that the universe has evolved from an initial singularity, as a FLRW solution; We do not know whether observations lead uniquely to a FLRW model, since observational cosmology is very limited.
* Successes: It has correctly explained the background microwave radiation and the He abundance in the universe.
* Problems: Flatness, horizon, monopole (if one includes particle physics), present value nbaryons / nphotons = 10–10, singularity, structure formation (these are partly initial conditions problems); Small anisotropies in the cmb.
* Solutions: Look for models in the usual theory with special properties (doesn't work); Completely different theory (?); Add some other ingredients (Steady State cosmology; Universal magnetic field; Cosmology and particle physics, including inflation; quantum cosmology).
* Alternatives: "Small universes", philosophically attractive but observationally hard to distinguish; > s.a. cosmic topology.
@ Accelerating: Albrecht & Skordis PRL(00)ap/99; Johri PRD(01) [tracker fields]; Neupane CQG(04)ht/03; > s.a. theories of acceleration.
@ As geodesic motion: Townsend & Wohlfarth CQG(04)ht [+ scalars]; Elias & Saa PoS-gq/07, PRD(07)gq [non-minimal coupling, anisotropic].
@ Related topics: Aguirre PRD(01)ap [and the anthropic principle]; > s.a. chaos in gravitation.

Homogeneous, Anisotropic > s.a. bianchi models [including Kasner and Mixmaster]; gödel solution; kantowski-sachs models; perturbations.
* Isometry group: An r (> 3)-parameter group of isometries with spacelike orbits; If r > 3 there is an isotropy group; Possibilities are R = 6, isotropic, FLRW models; or r = 4, local rotational symmetry.
@ General references: Nilsson et al ApJL(01)ap/99 [metric vs radiation isotropy]; Lim et al CQG(01)gq/99 [with isotropic cmb]; Stavrinos et al GRG(08)gq/06 [weak anisotropy].
@ Rotating: Obukhov in(00)ap; Chrobok et al PRD(01)gq; Carneiro GRG(02)gq/00.
@ Related topics: Vollick GRG(03)ht/01 [Born-Infeld electrodynamics + cosmological constant]; Hervik CQG(02)gq [5D]; > s.a. semiclassical general relativity [isotropization].

Inhomogeneous Models > s.a. cosmological acceleration and perturbations; information; numerical models.
* Idea: Slightly inhomogeneous models, such as perturbations off FLRW models, are used to write down corrections to the Friedmann, equation, verify predictions of inflation, and understand light propagation in a stochastic situation; Highly inhomogeneous models such as the swiss-cheese models (including the Einstein-Straus model) are used to find local effects of the overall expansion and other specific issues; Both types can be studied using exact solutions as models or approximation methods such as averaging.
* Other examples: Spherical models like the Stephani model and the Lemaître-Tolman-Bondi models, hierarchical models.
@ General references: Ellis in(93); Ibáñez & Olasagasti CQG(98) [and isotropization]; Tanimoto PTP(99)gq [and criticality]; Buchert GRG(00)gq/99, et al PRD(00)ap/99 [effect on average]; Clarkson et al GRG(03) [and the Copernican principle]; Berger CQG(04) [local Mixmaster dynamics]; Ellis CQG(11)-a1103 [significance for cosmology]; Bolejko et al CQG(11)-a1102 [rev]; Buchert CQG(11)-a1103 [non-perturbative effects]; Hellaby & Walters a1708 [observables].
@ And phenomenology: Kantowski et al ap/00 [distance vs z]; Canfora & Troisi GRG(04)ap/03 [structure formation]; Moffat JCAP(05)ap [acceleration and cmb]; Chuang et al CQG(08) [acceleration]; Hellaby PoS-a0910 [overview]; Clarkson & Maartens CQG(10)-a1005 [rev]; Hellaby JCAP(12)-a1203; Mishra et al PRD(12)-a1206 [and type-Ia supernovae]; Skarke PRD(14)-a1407 [evolution and acceleration, non-perturbative].
@ N-body models: Clifton CQG(11)-a1005 [without averaging, many equally-spaced masses]; Clifton et al PRD(12)-a1203 [quantification of backreaction].
@ Methods and solutions: Futamase PRL(88) [clumpy universe]; Krasiński 97; Yasuno et al CQG(01) [from gluing]; Uggla et al PRD(03)gq [framework]; Abdalla & Chirenti PhyA(04) [extremely inhomogeneous]; Ibáñez & Jhingan PRD(04)gq [renormalization group approach]; Lim PhD(04)gq [pfluid + cosmological constant]; Imponente & Montani AIP(06)gq [generic behavior]; Fernández-Jambrina & González-Romero in(07)-a0904 [non-singular]; di Teodoro & Villalba IJTP(08) [asymptotic symmetries]; Ferreira PLB(10)-a1006 [locally anisotropic, expanding]; Krasiński APPB-a1112-conf [comments on misunderstandings]; Klinger CQG(16)-a1512 [with no symmetries, singularities and billiards]; synopsis Phy(16) [results of relativistic numerical simulations].
> Other models: see perturbations and cosmological averaging; generalized FLRW models; solutions with matter; Stephani Model; Swiss-Cheese Models.
> Related topics: see Ricci Flow; tests of general relativity with light; types of spacetimes [cylindrical].


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