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].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 23 may 2021