De Sitter Space and Spatial Topology

TL;DR

This paper simplifies and generalizes previous results on initial data evolving into de Sitter spacetimes, providing explicit examples and analyzing the global evolution of wormhole initial data.

Contribution

It simplifies and extends prior work on initial data leading to de Sitter spacetimes, and analyzes the global evolution of wormhole initial data.

Findings

Explicit examples of locally de Sitter domains of development

Global time evolution of wormhole initial data solved

Universal covers not embeddable in de Sitter space

Abstract

Morrow-Jones and Witt have shown that generic spatial topologies admit initial data that evolve to locally de Sitter spacetimes under Einstein's equations. We simplify their arguments, make them a little more general, and solve for the global time evolution of the wormhole initial data considered by them. Finally we give explicit examples of locally de Sitter domains of development whose universal covers cannot be embedded in de Sitter space.