Phase Spaces for asymptotically de Sitter Cosmologies

Abstract

We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension $d\ge 3$. 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 $\pm i\frac{3\ell }{2G}$. 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 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 $\Lambda >0$ Einstein-Hilbert gravity due to the existence of a family of `wormhole' solutions labeled by their angular momentum, a mass-like parameter ${\theta }_0$, the topology of future infinity ($I^{+}$), and perhaps additional internal moduli. These solutions are $\Lambda >0$ analogues of BTZ black holes and exhibit a corresponding mass gap relative to empty de Sitter.

References in corpus (1)

• Asymptotic Symmetries and Charges in De Sitter Space

Cited by in corpus (11)

• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Asymptotics with a positive cosmological constant: I. Basic framework
• Implications of a positive cosmological constant for general relativity
• Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' condition
• Baby de Sitter Black Holes and dS${}_3$/CFT${}_2$
• Conserved charges in asymptotically de Sitter spacetimes
• Charges, conserved quantities and fluxes in de Sitter spacetime
• Combing gravitational hair in 2+1 dimensions
• Four-Dimensional Entropy from Three-Dimensional Gravity
• Regge-Teitelboim analysis of the symmetries of electromagnetic and gravitational fields on asymptotically null spacelike surfaces
• Issues about Cosmological Ward Identities