Einstein flow with matter sources: stability and convergence

TL;DR

This paper investigates the stability and convergence of Einstein flows with matter sources, extending previous vacuum studies to determine if matter influences the universe's tendency toward homogeneity and isotropy.

Contribution

It introduces matter sources into Einstein flow models to analyze their impact on the universe's asymptotic behavior, building on prior vacuum-based stability results.

Findings

Matter sources do not prevent the universe from evolving towards homogeneity.

The stability of Einstein flow with matter sources is established.

Convergence towards isotropic states is demonstrated in the presence of matter.

Abstract

Two recent articles \cite{ashtekar2015general, moncrief2019could} suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein-$\Lambda$ flow if a positive cosmological constant $\Lambda$ is included) which suggests that many closed (compact without boundary) manifolds that do not support homogeneous and isotropic metrics \textit{at all} will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. These studies however did not include matter sources. Therefore the aim of the present study is to include suitable matter sources and investigate whether one is able to draw a similar conclusion.