Uniqueness of de Sitter space

All inextendible null geodesics in four-dimensional de Sitter space dS4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS4 are eternal, i.e. extend from future infinity all the way back to past infinity . We show that the property of having a null line (inextendible achronal null geodesic) that extends from to characterizes dS4 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.