Uniqueness of de Sitter space

TL;DR

This paper characterizes four-dimensional de Sitter space as the unique spacetime with certain null geodesic and horizon properties, extending the result to include some matter models.

Contribution

It proves that de Sitter space uniquely exhibits null lines connecting past and future infinity among a broad class of spacetimes.

Findings

All null geodesics in dS^4 are complete and achronal.

De Sitter space is characterized by the existence of null lines from scri^- to scri^+.

The characterization extends to some matter-filled spacetimes.

Abstract

All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a null line (inextendible achronal null geodesic) that extends from scri^- to scri^+ characterizes dS^4 among all globally hyperbolic and asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations with positive cosmological constant. This result is then further extended to allow for a class of matter models that includes perfect fluids.