Remarks on inhomogeneous anisotropic cosmology

TL;DR

This paper examines how mean curvature flow affects inhomogeneous and anisotropic cosmologies, revealing potential singularities and limitations of existing theorems on cosmic recollapse, with implications for numerical inflation models.

Contribution

It provides a detailed analysis of mean curvature flow in Lorentzian manifolds, highlighting conditions under which singularities form and existing recollapse theorems may fail.

Findings

Singularities can develop during cosmic evolution.

Theorems preventing recollapse may not hold in inhomogeneous cases.

Inhomogeneities influence the evolution of spatial scalar curvature.

Abstract

Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow of spacelike surfaces in Lorentzian manifolds. We show that singularities may form during cosmic evolution and the theorems forbidding the global recollapse lose their validity. The time evolution of the spatial scalar curvature that may kinematically prevent the recollapse is determined in normal coordinates, which shows the impact of inhomogeneities explicitly. Our analysis indicates a caveat in numerical solutions that give rise to inflation.