Mass, Entropy and Holography in Asymptotically de Sitter Spaces

TL;DR

Balasubramanian, de Boer, and Minic develop a Brown–York-type boundary stress tensor framework for asymptotically de Sitter spaces, enabling definitions of mass and conserved charges on I± and motivating a possible dS/CFT dual. They compute masses for Schwarzschild–de Sitter in 4D/5D and Kerr–de Sitter in 3D, revealing that de Sitter space has maximal mass and proposing a mass bound linked to the entropy bound. In 3D they show a Cardy-like count using the central charge reproducing Kerr–de Sitter entropy for conical defects, while in higher dimensions they discuss a holographic c-function and RG/cosmology correspondence, highlighting subtleties like nonunitarity. The work suggests a consistent qualitative picture where de Sitter entropy arises from a finite density of dual states and time evolution corresponds to RG flow, laying groundwork for a precise dS/CFT framework and clarifying where further development is needed.

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.