The inverse mean curvature flow in Robertson-Walker spaces and its application to cosmology

TL;DR

This paper studies the inverse mean curvature flow in Robertson-Walker spacetimes, demonstrating it can smoothly connect big crunch and big bang phases under certain conditions, with an example showing limited regularity in general.

Contribution

It establishes conditions under which the inverse mean curvature flow provides a smooth transition between cosmological singularities in Robertson-Walker spaces.

Findings

Rescaled inverse mean curvature flow smoothly transitions from big crunch to big bang.

In general, the transition flow is only of class C^3.

Provides an example illustrating limited regularity of the transition flow.

Abstract

We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing that in general the transition flow is only of class $C^3$.