Bianchi I "asymptotically Kasner" solutions of the Einstein scalar field equations

TL;DR

This paper analyzes the conditions under which Bianchi I solutions of Einstein's equations with a scalar field become asymptotically Kasner near the singularity, providing theoretical criteria and explicit examples.

Contribution

It establishes necessary conditions on the scalar field potential for solutions to be asymptotically Kasner and offers explicit and numerical examples of such space-times.

Findings

Necessary conditions on potential for Kasner asymptotics

Explicit examples of asymptotically Kasner solutions

Numerical simulations supporting theoretical results

Abstract

In this work we investigate the asymptotic behaviour of solutions to the Einstein equations with a minimally coupled scalar field. The primary focus of the present paper here establishing under what conditions a solution becomes "asymptotically Kasner" sufficiently close to the initial singularity. To address this question we restrict our attention to Bianchi I space-times. By restricting our attention to a strictly monotonic scalar field we are able to provide necessary conditions on a potential so that the resulting solution is asymptotically Kasner. Moreover, we provide both explicit and numerical examples of asymptotically Kasner space-times.