Cosmological Models in General Relativity  

Homogeneous and Isotropic > s.a. observational cosmology; friedmann equation; FRW models; Milne Universe; quintessence.
* Standard model: Based on the cosmological principle, it predicts that the universe has evolved from an initial singularity, as a FRW solution; We do not know whether observations lead uniquely to FRW, 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 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.
* Cardassian expansion: An accelerating, quintessence model, in which the Friedmann equation becomes H2 = a new function of the energy density; The universe is flat, matter dominated, and accelerating, and the distance-redshift relation predictions can be very different from that of generic quintessence models.
@ Accelerating: Albrecht & Skordis PRL(00)ap/99; Johri PRD(01) [tracker fields]; Neupane CQG(04)ht/03; > s.a. acceleration.
@ Cardassian expansion: Freese & Lewis PLB(02)ap; Freese NPPS(03)hp/02; Gondolo & Freese PRD(03)hp/02 [fluid interpretation]; Das & Das PRD(03) [WMAP constraints]; Wang et al ApJ(03)ap [and supernova data]; Alcaniz et al ApJ(05)ap [constraints from lens statistics]; Freese NAR(05)ap; Koivisto et al PRD(05) [cmb spectrum]; Lazkoz & León PRD(05) [exponential potentials]; Szydlowski & Czaja AP(05) [behavior]; Liu et al PLB(06)ap/05 [exponential]; Wang & Wu PLB(09) [observational constraints].
@ As geodesic motion: Townsend & Wohlfarth CQG(04)ht [+ scalars]; Elias & Saa PoS-gq/07, PRD(07)gq [non-minimally coupling, anisotropic].
@ Related topics: Aguirre PRD(01)ap [and anthropic principle].

Homogeneous, Anisotropic > s.a. bianchi models [including Kasner and Mixmaster]; gödel solution; kantowski-sachs models.
* 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, FRW 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 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. acceleration; cosmology in general relativity [smoothing]; information; Ricci Flow; types of spacetimes [cylindrical].
@ Methods and solutions: Futamase PRL(88) [clumpy universe]; Krasinski 97; Perjés AdP(00)gq/99-in [with perfect fluids]; 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, 1 spatial degree of freedom]; Imponente & Montani gq/06-in [generic behavior]; Fernández-Jambrina & González-Romero in(07)-a0904 [non-singular]; di Teodoro & Villalba IJTP(08) [asymptotic symmetries].
@ Issues: 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 Copernican principle]; Berger CQG(04) [identifying local Mixmaster dynamics[.
@ 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]; > s.a. Stephani Model.

Without Singularity > s.a. cosmological perturbations; inflationary scenarios.
@ Bounces: Molina-París & Visser PLB(99)gq/98 [Tolman]; Solomons et al CQG(06)gq/01, CQG(06) [Kantowski-Sachs, Bianchi]; Peter & Pinto-Neto PRD(02) [evidence against]; Cartier et al PRD(03)ht; Stachowiak & Szydlowski PLB(07)gq/06 [modified Friedmann equation]; Novello & Perez Bergliaffa PRP(08)-a0802 [rev]; Falciano et al PRD(08)-a0802; > s.a. energy conditions, friedmann equation, higher-order gravity, Horava Gravity, relativistic cosmology; wormholes.
@ Cyclic / oscillating: Barrow & Dabrowski MNRAS(95); Dadhich & Raychaudhuri MPLA(99)gq; Steinhardt & Turok PRD(02)ht/01, PRD(02)ht/01, ap/02 [with acceleration and recontraction]; Khoury et al PRL(04)ht/03; Brown et al JCAP(08)-ap/04 [phantom, brane-inspired]; Rendall CQG(07) [with massive scalar fields]; Clifton & Barrow PRD(07)gq [unlikely explanations of flatness]; Frampton MPLA(07)-a0705 [infinite past]; > s.a. cosmic strings; types of inflation.
@ Emergent: Ellis et al CQG(04)gq/03 [static for t → –]; Ellis & Maartens CQG(04).
@ Related topics: Senovilla PRL(90), PRD(96); Chinea at al PRD(92); Fakir gq/98; Wagh ap/02 [inhomogeneous]; Fernández-Jambrina GRG(05)gq [non-rotating pfluids]; Dechant et al PRD(09)-a0809 [quasi-regular singularity].

Other Fields and / or Cosmological Constant > s.a. anti de sitter spacetime; bianchi models; de sitter spacetime; scalar-tensor theories.
@ Einstein-Yang-Mills, FRW-spherical symmetry: Gal'tsov & Volkov PLB(91); Darian & Künzle JMP(97); Rudolph et al JMP(99) [+ Dirac]; Breitenlohner et al PLB(00)gq [+ Higgs, static; Füzfa CQG(03)gq [instability]; Gal'tsov a0901-in [non-abelian condensates and dark energy].
@ Einstein-scalar: Williams et al gq/04 [isotropic and anisotropic]; Cannata et al PLB(09) [with singularity at finite scale factor].
@ Quintessence / dark energy: Gu & Hwang PLB(01)ap, ap/01; Wetterich ap/01; González-Díaz PRD(02)ht; Alam et al MNRAS(03)ap; Gruppuso & Finelli PRD(06)ht [dust + dark energy]; > s.a. cosmological constant.
@ Closed models: Lasenby & Doran PRD(05)ap/03 [with inflation]; Heinzle et al PRD(05)gq/04 [Bianchi IX and Kantowski-Sachs pfluid].
@ Related topics: Tsamis & Woodard PLB(98) [expansion rate]; Krauss & Turner GRG(99)ap [future]; Liu & Wesson ApJ(01)gq [varying cosmological constant]; Emoto et al PTP(02)ht [Einstein-electroweak]; > s.a. Chameleon Fields; chaos in gravitation; Phantom Fields.

Other Theories / Models > s.a. cosmology [unconventional]; gravitation; string phenomenology; supergravity.
* Goals: Need models which are only statistically homogeneous and isotropic; Verify inflation; Understand light propagation in a stochastic situation.
* Types: Inhomogeneous anisotropic (e.g., Stephani model), hierarchical.
@ 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].
@ Classification, overviews: Fischer GRG(96); Coley gq/99-in, Wainwright & Lim JHDE(05)gq/04 [dynamical systems].
@ Fractal: Pompilio & Montuori CQG(02)ap/01; > s.a. fractal.
@ Higher-dimensional: Jantzen in(87)gq/03; Paul PRD(01)gq [viscous fluid]; Chakraborty & Debnath IJMPD(04) [Szekeres metric with pfluid and cosmological constant]; > s.a. branes.
@ 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. 3D general relativity.
> Other theories: see Barker's Theory; brane cosmology [including ekpyrotic]; Lyra Geometry; modified general relativity; multiverse; perturbations; relativistic cosmology [varying constants]; types of singularities [including sudden].

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