General behaviour of Bianchi VI_0 solutions with an exponential-potential scalar field

TL;DR

This paper studies Bianchi VI_0 cosmological solutions with an exponential scalar field potential, revealing conditions for inflationary behavior, singular solutions, and stability of anisotropic solutions based on the potential's exponent.

Contribution

It provides a comprehensive analysis of Bianchi VI_0 solutions with exponential potentials, identifying inflationary, singular, and stable solutions depending on the potential parameter k.

Findings

Power-law inflation occurs when k^2<2.

Singular solutions exist for all k^2 values.

Stable anisotropic solutions are found for 2<k^2.

Abstract

The solutions to the Einstein-Klein-Gordon equations without a cosmological constant are investigated for an exponential potential in a Bianchi VI_0 metric. There exists a two-parameter family of solutions which have a power-law inflationary behaviour when the exponent of the potential, k, satisfies k^2<2. In addition, there exists a two-parameter family of singular solutions for all k^2 values. A simple anisotropic exact solution is found to be stable when 2<k^2.