Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation

TL;DR

This paper investigates the evolution of anisotropic universes with scalar fields, showing that isotropy can be achieved without inflation in Bianchi I models and confirming known results about inflation leading to isotropy.

Contribution

It demonstrates that in Bianchi I universes, isotropization can occur without inflation and identifies new critical points and exact solutions, expanding understanding of anisotropic universe evolution.

Findings

Isotropy can be reached without inflation in Bianchi I models.

New critical points lead to novel exact solutions.

Numerical results confirm asymptotic behaviors.

Abstract

We study the Einstein-Klein-Gordon equations for a convex positive potential in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing the inherent properties of the system of differential equations, the study of the asymptotic behaviors of the solutions and their stability is done for an exponential potential. The results are compared with those of Burd and Barrow. In contrast with their results, we show that for the BI case isotropy can be reached without inflation and we find new critical points which lead to new exact solutions. On the other hand we recover the result of Burd and Barrow that if inflation occurs then isotropy is always reached. The numerical integration is also done and all the asymptotical behaviors are confirmed.