de Sitter Spacetime| de Sitter Spacetime |
In General
> s.a. anti-de sitter space; ads-cft
[including dS-cft]; cosmological constant.
$ Def: A cosmological solution
of Einstein's equation with positive cosmological constant (for Λ < 0,
see > anti-de sitter spacetime), and line element
ds2 = −dt2 + H−2 cosh2(Ht) dΩ32, with H 2 = Λ/3 , amin = H−1 = (3/Λ)1/2,
the geometry of a Lorentz hyperboloid in 5D Minkowski space;
The symmetry group is SO(4, 1) (de Sitter group).
* Topology: \(\mathbb R\)
× S3, spatially compact [@ Mitskevich
& Senin SPD(82)].
* Infinity:
\(\cal I\)± are spacelike;
The spacetime has future and past event and particle horizons.
@ General references: in Schrödinger 56;
Spradlin et al ht/01-ln;
Bousso ht/02-fs [quantum aspects];
Kim et al ht/02 [classical, rev];
Schmidt AHA(05)gq [history];
Cuzinatto et al AJP(11)jun-a1009 [Lenz-Sommerfeld-type argument].
@ Geometry:
Parikh PLB(02) [new coordinates];
Kasedou JGP(10) [spacelike submanifolds of codimension 2];
Anninos et al CQG(11) [asymptotic symmetries and charges at null infinity];
Pascu a1211 [common coordinate charts];
Tod a1505 [and Penrose's quasi-local mass];
> s.a. coordinates [Fermi normal coordinates].
@ In quantum gravity:
Bousso PRD(99) [1-loop];
Witten ht/01-conf;
Klemm & Vanzo JCAP(04)ht ["quantum gravity in de Sitter space"];
Giddings & Marolf PRD(07)-a0705;
Einhorn & Jones JHEP(17)-a1606 [zero modes in metric conformal fluctuations];
Brahma et al a2007 [as a coherent state];
> s.a. quantum cosmology.
@ Related topics: Parikh et al PRD(03)ht/02 [elliptic, dS/\(\mathbb Z\)2];
Aledo & Romero DG&A(03) [3D, compact space];
McInnes JHEP(03)ht [S3 vs \({\mathbb R}{\rm P}^3\)];
Mbarek & Paranjape PRD(14)-a1407 [negative-mass bubbles];
Nouri-Zonoz et al PRD(15)-a1409 [with dark fluid or cosmological constant];
Russo & Townsend a1904
[compactification from D > 4 dimensions to de Sitter space];
> s.a. Hypersurfaces.
> Online resources:
see Wikipedia page.
Phenomenology
> s.a. fields and particles in de sitter spacetimes; inflation;
kinematics in special relativity [twin paradox]; radiation.
* Entropy: It can be associated
with the horizon, and in 2+1 calculated using Carlip's SL(2, \(\mathbb C\))
Chern-Simons theory method.
@ Thermodynamics:
Maldacena & Strominger JHEP(98) [entropy];
Wang & Huang MPLA(01) [path-integral approach];
Danielsson & Olsson JHEP(04)ht/03 [thermalization];
Takook AP(16)-a1306 [entropy of quantum fields];
Ulhoa & Spaniol JoG(16)-a1312 [entropy];
Podolskiy a1801 [entropy, from soft states].
@ Stability:
Abbott & Deser NPB(82) [canonical];
Faraoni PRD(05)gq,
Faraoni & Nadeau PRD(05)gq [in modified gravity and scalar-tensor];
Faraoni & Jensen CQG(06)gq [criterion, and dark energy/scalar-tensor gravity];
Parikh PRD(11)-a0909 [increased instability in Einstein-Gauss-Bonnet theory];
Copsey & Mann PRD(10)-a1001 [higher odd-dimensional, non-Kaluza-Klein bubbles of nothing];
Huang et al MPLA(10)-a1003 [in Hořava gravity];
Bander PRD(10)-a1003 [2D, with interacting fields];
Cognola et al a1006-MG12,
PRD(11) [in modified gravity];
Mena JPA(10)-a1006 [second-order perturbations of dust solution];
Elizalde et al PRD(12)-a1110,
PoS(11)-a1202 [in non-local cosmological models];
Anderson & Mottola PRD(14)-a1310,
PRD(14)-a1310
[global de Sitter space is unstable even for a massive free field theory];
> s.a. modified gravity;
semiclassical gravity; vacuum energy.
@ Quantum instability: Ho & Hsu JHEP(15)-a1501;
Rajaraman PRD(16)-a1608;
Matsui JCAP(19)-a1806 [from the conformal anomaly, below the Planck Scale].
@ Analogs in condensed matter: Fedichev & Fischer PRL(03)cm [and Hawking radiation];
Weinfurtner GRG(05)gq/04-conf.
Asymptotically de Sitter Spacetimes
> s.a. black-hole solutions; gravitational-wave
propagation; gravitational-wave solutions.
@ General references: Friedrich JGP(86);
Firouzjahi & Leblond JCAP(03)ht/02 [and aAdS];
Faraoni PRD(04)gq [de Sitter as attractor for gravity theories];
Galloway CM-gq/04-conf [conformal infinity and singularities];
Lübbe & Valiente Kroon CQG(09)-a0903 [existence];
Anninos IJMPA(12)-a1205 [overview of some issues];
Ashtekar et al CQG(14)-a1409
+ CQG+ [basic framework for asymptotics];
Kastor et al CQG(17)-a1608 [asymptotically future de Sitter];
Aneesh et al CQG(19)-a1902 [conserved charges];
Ashtekar & Bahrami PRD(19)-a1904 [the 'no-incoming radiation' condition];
Fernández-Álvarez & Senovilla a2105 [asymptotic structure, new approach].
@ Mass, energy: Kastor & Traschen CQG(02)ht [positive energy];
Dolan a1808;
Almaraz & Lopes de Lima a1811.
@ And matter fields: Medved CQG(02)ht [with dust, and holography];
Leblond et al JHEP(03)ht/02 [massive scalar fields];
Meissner a0901 [with point mass];
Ashtekar et al PRD(15)-a1506.
@ Stability: Bruni et al CQG(02) [second-order perturbations of FLRW spacetimes].
> Related topics: see
Alexandrov Sets and causal structures [volumes of causal
intervals]; multipole moments; Quadrupole Formula.
Other Similar Spacetimes and Generalizations
> s.a. differential geometry [fuzzy de Sitter];
higher-order theories.
@ References: Giambò CQG(02) [anisotropic matter];
Schleich & Witt CJP(08)-a0807,
Randono CQG(10)-a0909 [locally de Sitter spacetimes];
Minkevich MPLA(11)-a1002 [with torsion];
> s.a. modified general relativity [de Sitter tangent group];
solutions of general relativity [topology].
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