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].

@ __G___{2}:
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*)+2*S* 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
*n*_{baryons} / *n*_{photons}
= 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(99)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 JCAP(18)-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].

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