Properties of homogeneous cosmologies in scalar tensor theories

TL;DR

This paper investigates how homogeneous but anisotropic cosmological models evolve towards isotropy within scalar-tensor theories, identifying conditions and behaviors that facilitate isotropisation, including effects of scalar fields and potentials.

Contribution

It introduces a classification of isotropisation processes in scalar-tensor cosmologies and provides general constraints and asymptotic behaviors for these models.

Findings

Three classes of isotropisation identified

Scalar fields can act as quintessence during isotropisation

Curvature influences late-time acceleration and quintessence

Abstract

We study the isotropisation of the homogeneous but anisotropic Bianchi class A models in presence of a minimally coupled and massive scalar field with or without a perfect fluid. To this end, we use the Hamiltonian formalism of Arnowitt, Deser and Misner(ADM) and the dynamical systems analysis methods. Our results allow to define three kinds of isotropisation called class 1, 2 and 3. We have specifically studied the class 1 and obtained some general constraints on scalar-tensor theories which are necessary conditions for isotropisation. The asymptotical behaviors of the metric functions and potential in the neighborhood of isotropy have also been determined when the isotropic state is reached sufficiently quickly. We show that the scalar field responsible for isotropisation may be quintessent and that the presence of curvature favor a late times acceleration and quintessence. Some applications are made with the well known exponential law potential by using our theoretical results but also by help of numerical analysis. The isotropisation process with a power law potential is also explored. We think this work represents a framework able to guide some future researches on the isotropisation of homogeneous models in scalar-tensor theories and we argue by discussing briefly about some recent results we have obtained in presence of a non minimally coupled scalar field or several scalar fields.