dS/CFT and spacetime topology

TL;DR

This paper explores topological restrictions on de Sitter spacetimes with positive cosmological constant that have regular conformal boundaries, extending ideas from AdS/CFT to de Sitter contexts.

Contribution

It establishes new topological constraints on de Sitter spacetimes with conformal boundaries, linking boundary properties to global spacetime topology.

Findings

Compact conformal boundary implies finite fundamental group.

Boundaries must admit metrics of positive scalar curvature.

Results relate to Euclidean AdS/CFT theorems by Witten and Yau.

Abstract

Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with $\Lambda>0$, which admit a regular past and/or future conformal boundary. For example we show that if $M^{n+1}$, $n \ge 2$, is a globally hyperbolic spacetime obeying suitable energy conditions, which is of de Sitter type, with a conformal boundary to both the past and future, then if one of these boundaries is compact, it must have finite fundamental group and its conformal class must contain a metric of positive scalar curvature. Our results are closely related to theorems of Witten and Yau hep-th/9910245 pertaining to the Euclidean formulation of the AdS/CFT correspondence.