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Higuchi, Katsunori; Niinobe, Yasuo; Yamamoto, Manabu; Iribe, Yoshimasa

doi:10.2208/journalam.8.117

Cited by 1 publication

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“…The purpose of this paper is to construct associated phase spaces (for both k = 0, −1) of asymptotically de Sitter solutions in d ≥ 3 spacetime dimensions for which the expected charges are finite and conserved. As there are claims [17][18][19][20][21][22] in the literature that the socalled 'dilatation symmetry' of the k = 0 patch is broken at the quantum level (though see [23][24][25][26][27][28][29][30][31]), it is particularly important to verify that this is indeed a symmetry of an appropriate classical gravitational phase space for k = 0.…”

Section: Introductionmentioning

confidence: 99%

Phase spaces for asymptotically de Sitter cosmologies

Kelly¹,

Marolf²

2012

Class. Quantum Grav.

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We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension d ≥ 3. One type contains solutions asymptotic to the expanding spatially-flat (k = 0) cosmological patch of de Sitter space while the other is asymptotic to the expanding hyperbolic (k = −1) patch. Each phase space has a non-trivial asymptotic symmetry group (ASG) which includes the isometry group of the corresponding de Sitter patch. For d = 3 and k = −1 our ASG also contains additional generators and leads to a Virasoro algebra with vanishing central charge. Furthermore, we identify an interesting algebra (even larger than the ASG) containing two Virasoro algebras related by a reality condition and having imaginary central charges ±i 3 2G . Our charges agree with those obtained previously using dS/CFT methods for the same asymptotic Killing fields showing that (at least some of) the dS/CFT charges act on a welldefined phase space. Along the way we show that, despite the lack of local degrees of freedom, the d = 3, k = −1 phase space is non-trivial even in pure Λ > 0 Einstein-Hilbert gravity due to the existence of a family of 'wormhole' solutions labeled by their angular momentum, a mass-like parameter θ 0 , the topology of future infinity (I + ), and perhaps additional internal moduli. These solutions are Λ > 0 analogues of BTZ black holes and exhibit a corresponding mass gap relative to empty de Sitter.

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