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Phase spaces for asymptotically de Sitter cosmologies


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 . 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 well-defined 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. © 2012 IOP Publishing Ltd.

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