Perturbations of FLRW Spacetimes  

In General > s.a. cosmology; FLRW models; perturbations in general relativity; relativistic cosmology [effects].
* Classification: A convenient decomposition of a perturbation is

\[ a(t)^{-2}\delta g_{ab} = \left(\matrix{\phi & -B_{,i} \cr -B_{,i} & \psi\,\delta_{ij} + E_{,ij}}\right)
+ \left(\matrix{0 & S_i \cr S_i & 2\,F_{i,j}}\right) + \left(\matrix{0 & 0 \cr 0 & H_{ij}}\right), \]

respectively a scalar, vector, and tensor perturbation; Here, Si and Fi are divergenceless 3-vectors.
* Gauge: Four of the 10 components can be gauged away, and four fixed using constraints, leaving two degrees of freedom; For calculations, the longitudinal gauge (E = B = Si = 0, metric perturbation diagonal) is often convenient, but in terms of physical insight the comoving gauge seems to be best.
* Vector perturbations: 2004, Usually dismissed, because they decay (they are a flux, and with the expansion...), but the situation is not very clear.
@ General references: Bardeen PRD(80) [gauge]; D'Eath AP(76); Ellis & Jaklitsch ApJ(89) [constraints]; Schön PRD(89); Ramírez & Kopeikin PLB(02)gq/01 [k = 0 hyperbolic pdes]; Bičák et al PRD(04)gq/03 [toroidal]; Durrer ap/04-ln; Sharma & Khanal IJMPD(14)-a1109 [in the NP formalism]; Uggla & Wainwright CQG(12)-a1112 [scalar]; Pavlov a1601 [intrinsic time].
@ Gauge-invariant: Ellis & Bruni PRD(89); Ellis et al PRD(89); Stewart CQG(90); Bombelli et al CQG(94); Durrer FCP(94)ap/93; Deruelle & Uzan IJTP(97)gq/98 [conservation laws]; Zimdahl CQG(97) [conserved quantities]; Kopeikin et al PLA(01)gq [dust, new approach]; Miedema & van Leeuwen gq/03/CQG, a1003-wd; Giesel et al CQG(10)-a0711.
@ Phenomenology: Fanizza et al JCAP(15)-a1506 [light propagation].
@ Related topics: Bashinsky & Bertschinger PRD(02)ap [dynamics]; Andersson & Moncrief in(04)gq/03 [global existence]; Nambu PRD(05)gq [long-λ, back-reaction]; Bičák et al PRD(07)-a0803 [and local inertial frames]; Baumann et al JCAP(11)-a1101 [scale-invariant and weakly coupled fluctuations].

Specific Models > s.a. cosmological perturbations [including higher-order gravity]; cosmological models.
@ Exact: Couch & Torrence GRG(96); Sopuerta PRD(99) [general, + flat dust models]; Castagnino et al IJTP(02) [k = 0 + scalar].
@ Gravitational waves: Waylen PRS(78) [in k = –1]; Couch & Torrence GRG(90), GRG(90) [progressing waves].
@ Bouncing models: Brandenberger et al PRD(02) [trans-lP physics]; Gordon & Turok PRD(03); Martin & Peter PRD(03)ht, PRL(04)ap/03, PRD(04)ht, gq/04; Deruelle & Streich PRD(04)gq; Deruelle gq/04; Gasperini et al NPB(04); Allen & Wands PRD(04); Pinto-Neto IJMPD(04)ht; Battefeld & Geshnizjani PRD(06)ht/05; Creminelli et al PRD(05); Cardoso & Wands PRD(08).
@ With varying constants: Barrow & Mota CQG(03)gq/02 [varying α].
@ Other models: Hwang & Noh CQG(02)ap/01 [multiple fields]; Khoury et al PRD(02)ht/01 [ekpyrotic]; Ullrich MS(07)-a0709 [fluids + cosmological constant].

Non-Linear, Second-Order
@ General references: Reula PRD(99)gq [exponential decay]; Mena et al IJMPA(02)gq-in [+ cosmological constant]; Noh & Hwang PRD(04)ap/03 [+ cosmological constant]; Langlois & Vernizzi PRL(05)ap [fully non-perturbative].
@ Gauge-invariant: Clarkson PRD(04) [and waves]; Bartolo et al JCAP(04)ap/03 [non-Gaussianity]; Nakamura gq/06-proc.
@ Localized: Wilson & Dyer GRG(07) [spherically symmetric overdense galaxy-like region].

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