Scalar curvature of spacelike hypersurfaces and certain class of cosmological models for accelerated expanding universes

TL;DR

This paper investigates the scalar curvature of spacelike hypersurfaces in generalized Robertson-Walker spacetimes, providing rigidity results and demonstrating their relevance as models for accelerated expanding universes under certain conditions.

Contribution

It offers new rigidity results for spacelike hypersurfaces and establishes these spacetimes as suitable models for accelerated expansion in cosmology.

Findings

Rigidity results for scalar curvature under specific assumptions

Generalized Robertson-Walker spacetimes satisfy null convergence condition

Models explain accelerated expanding universes

Abstract

We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson-Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On the other hand, we show that this family of spacetimes provides suitable models obeying the null convergence condition to explain accelerated expanding universes.