Perturbations of FLRW Spacetimes| Perturbations of FLRW Spacetimes |
In General > s.a. cosmology;
FLRW models; perturbations in general relativity
and in quantum cosmology; 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 LNP(05)ap/04;
Sharma & Khanal IJMPD(14)-a1109 [in the NP formalism];
Uggla & Wainwright CQG(12)-a1112 [scalar];
Pavlov a1601 [intrinsic time];
Noh et al PRD(20)-a2003 [linearization instability].
@ 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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