Friedmann-Robertson-Walker Spacetimes  

General Properties of the Metric > s.a. [bianchi models]; cosmological models [geodesics]; geometric quantities of frw metrics.
* Idea: A homogeneous and isotropic metric, characterized by one of three types of 3D constant curvature spatial geometries (open k = –1, flat k = 0, or closed k = 1), and a function a(t) representing its fiducial size at time t.
* Line element: In the proper time gauge, it is of the form

ds2 = –d2 + a()2 [d2 + f 2() (d2 + sin2 d2)] = –dt2 + a(t)2 [dr2/(1–kr2) + r2 d2] ,

where f 2() = sin2 if k = 1, 2 if k = 0, and sinh2 if k = –1; > s.a. spherical symmetry.
* Singularities: For k > 0, a point; For k 0, an infinite manifold.
* Useful quantities: Hubble expansion factor H:= a·/a; Satisfies (1/6) R = a··/a + H2 = k/a2.
* Scalar curvature: Using conformal time,

R = 6 a··/a – 2 (2 ff '' + f '2–1)/(af)2 .

@ References: Hall CQG(00) [projective symmetries]; Camci & Barnes CQG(02)gq/01 [Ricci collineations]; Rindler PLA(00) [finite-volume foliations in k < 0]; > s.a. cosmological expansion; types of singularities [including sudden]; world function.

With Fluid Matter > s.a. branes; canonical and covariant quantum gravity; cosmological models in general relativity; FRW quantum cosmology.
* Idea: The corresponding family of cosmological solutions of Einstein's equation generalize the friedmann solutions.
* Special cases: For the case of a viscous fluid, the only term allowed by the symmetry is bulk viscosity.
@ Fluid: Vajk JMP(69); Elbaz et al GRG(97) [Hamiltonian]; Faraoni AJP(99)phy; Di Prisco et al PRD(01)gq/00 [dissipative]; Lima AJP(01)ap; Rosu et al JPA(03)mp/01 [barotropic, Riccati equation]; Gessner & Dehnen ap/02/ApJ [2 fluids]; Mak & Harko IJMPD(04)gq/03 [viscous, stiff]; Wiltshire gq/03 [rotating]; Banks et al PRD(05)ht/04 [k = 0, radiation, quantum]; Szydlowski & Hrycyna AP(07) [dissipative].
@ Fluid + cosmological constant: Silbergleit gq/01; Kristjánsson & Thorlacius JHEP(02)ht/02 [different dimensionalities]; Berbena et al gq/06-in; Aldrovandi et al FP(06).
@ Fluid + scalar: van den Hoogen et al CQG(99)gq; Arias et al gq/02, Mak & Harko IJMPD(02)gq [quintessence]; Dehnen et al G&C(03) [k = 0]; Miritzis CQG(03)gq; D'Ambroise & Williams ht/06 [equivalent to non-linear Schrödinger equation].
@ Unconventional fluid: Aguirregabiria & Lazkoz PRD(04)ht [tachyonic + barotropic, tracking].
@ Matter + cosmological constant: Dabrowski AP(96)gq/95 [oscillating]; Hamilton MNRAS(01)ap/00 [expansion rates]; Gudmundsson & Björnsson ApJ(02)ap/01; Lake PRL(05) [with = 1].
@ In Regge calculus: Collins & Williams PRD(73) [3+1]; Brewin CQG(87); De Felice & Fabri gq/00, gq/01 [600-cell polytope].
@ Related topics: Tomaschitz JMP(93) [dispersion]; Zecca JMP(96) [separation of variables]; Martin et al JHEP(05)gq/00 [topology-change Green function]; Kirchner & Ellis CQG(03) [prob measure]; Gambini & Pullin CQG(03) [discretized].

Other Fields and Effects > s.a. chaotic motion; phenomenology [including tails], wave solutions and propagation; thermodynamics.
@ Scalar field: Schmidt AN(90)gq/01 [k = 1, massive]; Kamenshchik et al IJMPD(97)gq/98 [including fractal]; Santiago & Silbergleit PLA(00)gq/98; Leach et al G&C(01) [integrability]; de Siqueira gq/01 [massive]; Khvedelidze & Palii CQG(01)gq [and spinor]; Figueiredo et al IJTP(02)gq [quintessence + scalar]; Williams & Kevrekidis CQG(03) [and Ermakov-Pinney equation]; Christodoulakis et al gq/03 [kg]; Maeda & Harada PLB(05)gq/04 [kink instability]; Berera & Ramos PRD(05)hp/04 [+ other]; Guo & Cai gq/05 [multi-scalar, evolution as geodesic]; Giambò et al JMP(06) [variational approach], a0802 [with general potential]; Maciejewski et al a0803 [integrability]; Reyes a0806 [spatially flat].
@ Scalar field, non-minimal coupling: Alberghi et al PRD(00)gq/99; Castagnino et al PRD(00)gq/99, PRD(02) [conformal]; Gunzig et al PRD(01)gq/00 [and superinflation]; Coelho et al JPA(08) [conformal, integrability].
@ Phantom: Singh et al PRD(03)ht; Chimento & Lazkoz PRL(03)gq; Guo et al PLB(04); Szydlowski et al PRE(05)ap/04; Johri PRD(04); Dabrowski & Stachowiak AP(06)ht/04.
@ Einstein-Yang-Mills: Henneaux JMP(82); Donets et al PRD(99)gq/98 [N = 2 susy]; Shchigolev & Samaroo GRG(04) [+ non-linear scalar].
@ Plane waves: Tsamis & Woodard CQG(03)ap/02 [k = 0 case].
@ Spinor / Dirac fields: Barut & Duru PRD(87); Epstein GRG(99) [k = 0 case]; Sarkar & Biswas IJMPA(00); Zecca NCB(03); Armendáriz-Picón & Greene GRG(03)ht; Vakili et al JCAP(05) [classical and quantum cosmology]; Balantekin & Dereli PRD(07)gq [Majorana fermion + scalar]; > s.a. cosmological constant [as fermion condensate].
@ Electromagnetic fields: Mashhoon PRD(73) [k = 1]; Hogan & Ellis CQG(97) [and gravitational waves]; Dariescu & Dariescu IJMPA(03); Haghighipour GRG(05) [asymptotic properties and tails]; Khanal CQG(06)ap/05 [+ Dirac, NP formalism]; > s.a. Proca, modified em theory and QED.
@ Stability: Szydlowski & Czaja PRD(04)ap/03 [Chaplygin gas]; Gorini et al PRD(05) [various fluids].
@ Related topics: Cavaglià & Vargas CQG(01) [from M-theory]; van Holten PRL(02) [Einstein-Higgs]; Zecca NCB(06) [arbitrary spin, separation of variables]; Bina et al a0709-IJTP [scalar with non-commutativity and minimal length]; > s.a. dark energy; modified quantum mechanics; tachyons.

Quantum Fields > s.a. entanglement examples; linearized quantum gravity; semiclassical gravity.
@ General references: Shirai & Wada NPB(88) [perturbations]; Guven et al PRD(89) & refs; Finelli et al CQG(99)gq [em + Dirac]; Bouhmadi-López et al PRD(02)gq [radiation + cosmological constant + perturbations]; > s.a. inflation.
@ Scalar field: Castagnino & Chimento GRG(86) [adiabatic vacuum]; Boyanovsky et al PRD(97); Lombardo et al MPLA(99)gq/98 [classical chaos and particle creation]; Redmount PRD(99)gq [massive, k < 0 FRW models]; Setare IJTP(04) [massive, particle creation and Casimir effect]; Tichavsky mp/06 [Hadamard condition]; Arteaga JPA(07), et al IJTP(07); Olbermann CQG(07)-a0704 [low-energy states]; Pascoal & Farina IJTP(07) [particle creation].

Related Metrics and Concepts, Other Theories > s.a. asymptotic flatness; chaotic metrics; perturbations; schwarzschild.
@ Asymptotically FRW: Shiromizu & Gen CQG(99)gq [at timelike infty]; Canfora & Troisi GRG(04) [and structure formation]; Pinto-Neto & Trajtenberg GRG(04)gq [asymptotically FRW, Hamiltonian]; > s.a. gravitational energy, schwarzschild.
@ With varying constants: Barrow et al PLB(02)gq [G and ]; Pradhan et al gq/06 [G and ]; > s.a. relativistic cosmology, varying constants.
@ Higher-dimensional and brane world: Nojiri et al IJMPA(02) [rev]; Khoury & Zhang PRL(02)ht; García & Carlip PLB(07) [n-dimensional].
@ Higher-order theories: Esposito NCB(89)gq/95 [R2 with torsion]; Sanyal PLB(02)gq, Miritzis JMP(03)gq [+ scalar], JMP(05)gq [+ pfluid + scalar, recollapse problem]; Clifton CQG(07)gq [4th-order, vacuum and fluid]; de Souza & Faraoni CQG(07)-a0706 [arbitrary f(R), phase space view].
@ Other theories: Minkevich & Garkun CQG(00) [metric-affine gravity]; Minkevich a0709 [Poincaré gauge theory of gravity]; > s.a. brans-dicke, friedmann equation, supergravity; Yilmaz.
@ Related topics: Barceló et al IJMPD(03)gq-GRF [cond-mat analogs]; Loran ht/05 [observing FRW in Minkowski?].

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