Phase Spaces for asymptotically de Sitter Cosmologies

TL;DR

This paper constructs phase spaces for asymptotically de Sitter spacetimes, identifies their asymptotic symmetries including Virasoro algebras, and explores non-trivial solutions analogous to BTZ black holes in three dimensions.

Contribution

It introduces new phase spaces for asymptotically de Sitter geometries with detailed symmetry analysis and finds novel algebraic structures and solutions in three dimensions.

Findings

Identified asymptotic symmetry groups including Virasoro algebras.

Found a larger algebra with two Virasoro algebras and imaginary central charges.

Discovered non-trivial wormhole solutions in 3D de Sitter gravity.

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.