Mass, Entropy and Holography in Asymptotically de Sitter Spaces

TL;DR

This paper introduces a new method to compute boundary stress tensors and charges in asymptotically de Sitter spaces, explores their holographic duals, and relates cosmological evolution to renormalization group flow.

Contribution

It proposes a novel prescription for boundary stress tensor calculation in dS spaces and explores implications for holography and cosmological entropy.

Findings

Masses of Schwarzschild-de Sitter black holes computed in 4 and 5 dimensions.

Masses and angular momenta of Kerr-de Sitter spaces in 3 dimensions calculated.

De Sitter spaces with mass greater than de Sitter likely have a cosmological singularity.

Abstract

We propose a novel prescription for computing the boundary stress tensor and charges of asymptotically de Sitter (dS) spacetimes from data at early or late time infinity. If there is a holographic dual to dS spaces, defined analogously to the AdS/CFT correspondence, our methods compute the (Euclidean) stress tensor of the dual. We compute the masses of Schwarzschild-de Sitter black holes in four and five dimensions, and the masses and angular momenta of Kerr-de Sitter spaces in three dimensions. All these spaces are less massive than de Sitter, a fact which we use to qualitatively and quantitatively relate de Sitter entropy to the degeneracy of possible dual field theories. Our results in general dimension lead to a conjecture: Any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity. Finally, if a dual to de Sitter exists, the trace of our stress tensor computes the RG equation of the dual field theory. Cosmological time evolution corresponds to RG evolution in the dual. The RG evolution of the c function is then related to changes in accessible degrees of freedom in an expanding universe.