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(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].

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