Isotropisation of Bianchi class A models with curvature for a minimally coupled scalar tensor theory

TL;DR

This paper investigates conditions under which Bianchi class A cosmological models with curvature become isotropic, highlighting the roles of scalar fields, late-time acceleration, and flatness in the evolution of the universe.

Contribution

It provides necessary conditions for isotropisation in Bianchi class A models with curvature within a scalar-tensor framework, including the behavior of metric functions and potential.

Findings

Isotropisation leads to power or exponential law of metric functions.

Potential vanishes as t^{-2} or approaches a constant.

Late-time accelerated expansion and flatness are required for isotropisation.

Abstract

We look for necessary isotropisation conditions of Bianchi class $A$ models with curvature in presence of a massive and minimally coupled scalar field when a function $\ell$ of the scalar field tends to a constant, diverges monotonically or with sufficiently small oscillations. Isotropisation leads the metric functions to tend to a power or exponential law of the proper time $t$ and the potential respectively to vanish as $t^{-2}$ or to a constant. Moreover, isotropisation always requires late time accelerated expansion and flatness of the Universe.