Exponential-Potential Scalar Field Universes II: The Inhomogeneous Models

TL;DR

This paper derives exact inhomogeneous cosmological solutions with exponential scalar field potentials, revealing inflationary phases, late-time homogenization, and persistent anisotropy, enriching understanding of scalar field cosmologies.

Contribution

It provides new exact solutions for inhomogeneous scalar field cosmologies with exponential potentials, analyzing their inflationary and homogenization behaviors.

Findings

Inflationary behavior occurs for k^2<2 in most cases.

Solutions tend to homogenize at late times for k^2>2.

None of the solutions become isotropic.

Abstract

We obtain exact solutions for the Einstein equations with an exponential-potential scalar field (\(V=\Lambda e^{k\phi}\)) which represent simple inhomogeneous generalizations of Bianchi I cosmologies. Studying these equations numerically we find that in most of the cases there is a certain period of inflationary behaviour for \(k^2<2\). We as well find that for \(k^2>2\) the solutions homogenize generically at late times. Yet, {\em none of the solutions} isotropize. For some particular values of the integration constants we find a multiple inflationary behaviour for which the deceleration and the inflationary phases interchange each other several times during the history of the model.