On the evolution of universes in quadratic theories of gravity

TL;DR

This paper investigates the stability and evolution of Bianchi universes in quadratic gravity theories, revealing isotropization mechanisms, conditions for de Sitter stability, and novel anisotropic inflationary behaviors.

Contribution

It provides a dynamical systems analysis of Bianchi universes in quadratic gravity, identifying stability conditions and discovering new anisotropic inflationary solutions.

Findings

Existence of an isotropic FRW universe as a past attractor.

Conditions for the stability of de Sitter solutions.

Discovery of new anisotropic inflationary behaviors.

Abstract

We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Due to the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic FRW universe acting as a past attractor. This may indicate that there is an isotropisation mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated centre manifold structure, and show that there exists a set of non-zero measure which has the Kasner solutions as a past attractor. Regarding the late-time behaviour, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behaviour with phantom-like behaviour. New types of anisotropic inflationary behaviour are found which do not have counterparts in general relativity.