Friedmann-Lemaître-Robertson-Walker Spacetimes  

General Properties
* Motivation: They approximate our universe extremely well; The spacetime metric is approximated by an FLRW metric to about 1 part in 104 or better on both large and small scales, except in the immediate vicinity of very strong field objects; Derivatives of the metric are not close to those of FLRW models, so there can be significant differences in the geodesics and curvature, but they do not produce significant backreaction effects on cosmological scales.
* 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; > s.a. geometry of FLRW metrics.
* Stability: These solutions are gravitationally unstable to inhomogeneous perturbations, and in the class of averaged inhomogeneous models.
@ General references: Hall CQG(00) [projective symmetries]; Camci & Barnes CQG(02)gq/01 [Ricci collineations]; Rindler PLA(00) [finite-volume foliations in k < 0]; Melia & Abdelqader IJMPD(09)-a0907 [observer-dependent coordinates and interpretation of observations]; Green & Wald CQG(14)-a1407 [as models for the universe]; > s.a. cosmological expansion [including interpretation]; world function.
@ Singularities: Singh Kohli a1602; > s.a. types of singularities [including sudden].
@ Stability: Szydłowski & Czaja PRD(04)ap/03 [Chaplygin gas]; Gorini et al PRD(05) [various fluids]; Roy et al CQG(11)-a1103 [dynamical-system analysis of the dark sectors]; Kouwn et al PRD(12)-a1103 [asymptotically static, generalized quintom models].
@ Particles and fields: Kelner et al PRD(11) [mechanics and kinetics]; Bini et al EPJC(13)-a1408 [test particles undergoing friction forces]; > s.a. geodesics; chaotic motion; fields in FLRW backgrounds [including quantum field theory, bounces].
@ Related topics: Katanaev MPLA(15)-a1511 [new definition of homogeneous and isotropic spacetime, and new type].
blue bullet Aspects of FLRW models: see friedmann equation; FLRW geometry; FLRW quantum cosmology.
blue bullet Related topics: see cosmological models in general relativity; perturbations; standard cosmological model.

With Fluid Matter > s.a. branes; canonical and covariant quantum gravity.
* Idea: The corresponding family of cosmological solutions of Einstein's equation generalize the friedmann solutions obtained for dust.
* Special cases: For the case of a viscous fluid, the only term allowed by the symmetry is bulk viscosity.
@ General references: Vajk JMP(69); Elbaz et al GRG(97) [Hamiltonian]; Faraoni AJP(99)aug-phy; Di Prisco et al PRD(01)gq/00 [dissipative]; Lima AJP(01)dec-ap; Rosu et al JPA(03)mp/01 [barotropic, Riccati equation]; Geßner & Dehnen ASS(03)ap/02 [2 fluids]; Mak & Harko IJMPD(04)gq/03 [viscous, stiff]; Wiltshire & Messenger GRG(03)gq [rotating]; Banks et al PRD(05)ht/04 [k = 0, radiation, quantum]; Szydłowski & Hrycyna AP(07) [dissipative].
@ Fluid + cosmological constant: Silbergleit gq/01; Kristjánsson & Thorlacius JHEP(02)ht/02 [different dimensionalities]; Berbena et al gq/06-conf; Aldrovandi et al FP(06); D'Ambroise & Williams JMP(10)-a1007 [modeled by a Bose-Einstein condensate]; Kumar ASS(11)-a1010 [perfect fluid and dark energy]; Sonego & Talamini AJP(12)aug-a1112 [qualitative study]; Ha et al GRG(12).
@ 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, Gumjudpai GRG(09) [non-linear Schrödinger equation formulation]; Szydłowski & Hrycyna JCAP(09)-a0811.
@ 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 Ω = 1].
@ In Regge calculus: Collins & Williams PRD(73) [3+1]; Brewin CQG(87); De Felice & Fabri gq/00, gq/01 [600-cell polytope]; Liu & Williams PRD(16)-a1501; Tsuda & Fujiwara a1612 [3D, with positive cosmological constant].
@ 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) [probability measure]; Gambini & Pullin CQG(03) [discretized].

Related Metrics and Concepts, Other Theories > s.a. asymptotic flatness; chaotic metrics; schwarzschild spacetime.
@ Asymptotically FLRW spacetimes: Shiromizu & Gen CQG(99)gq [at timelike infinity]; Canfora & Troisi GRG(04) [and structure formation]; Pinto-Neto & Trajtenberg GRG(04)gq [Hamiltonian]; > s.a. gravitational energy; schwarzschild solution.
@ Generalizations: Visser CQG(15)-a1502 [conformally FLRW cosmologies]; Mantica & Molinari IJGMP-a1612 [spatially non-homogeneous].
@ With varying constants: Barrow et al PLB(02)gq [G and α]; Pradhan et al RJP(07)-gq/06 [G and Λ]; > 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]; Clifton PRD(08)-a0807 [higher powers of R]; Farajollahi et al GRG(11)-a1005, Domazet et al IJMPD(13)-a1203 [f(R) theories].
@ Scalar-tensor gravity: Kuusk et al IJMPA(09)-a0810-conf; Järv et al PRD(12)-a1112 [with dust matter]; Dogru & Baykal a1209; > s.a. brans-dicke theory.
@ Non-local gravity: Farajollahi & Milani IJTP(11)-a1103; Dimitrijevic et al a1202-proc; Dimitrijevic AMC(16)-a1604 [cosmological solutions].
@ Other theories: Minkevich & Garkun CQG(00) [metric-affine gravity]; Minkevich AFLB(07)-a0709 [Poincaré gauge theory of gravity]; Sáez-Gómez PhD(11)-a1104; Pérez-Payán et al PRD(13)-a1111 [scalar field cosmology with deformed phase space]; Asselmeyer-Maluga & Król a1201 [with exotic differentiable structure, changing value of k]; Gannouji et al JCAP(11) [in Weyl extension of general relativity]; Myrzakulov EPJC(12)-a1207 [f(R,T) gravity]; Much a1608 [deformed]; > s.a. friedmann equation; hořava gravity; MOND; supergravity; Yilmaz Theory.
@ Related topics: Barceló et al IJMPD(03)gq-GRF [condensed-matter analogs]; Loran ht/05 [observing FLRW in Minkowski space?]; Levrino & Tartaglia SCPMA(14)-a1205 [analogy with generalized elasticity theory]; Upadhyay PTEP(15)-a1507 [superspace description]; > s.a. metric matching.


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