Phase space of modified Gauss-Bonnet gravity

TL;DR

This paper explores the phase space and dynamical behaviors of modified Gauss-Bonnet gravity in FLRW cosmologies, identifying conditions for accelerated expansion and analyzing stability issues related to higher-order derivatives.

Contribution

It introduces a new method to analyze the phase space of Gauss-Bonnet gravity and discusses the conditions for acceleration and singularities in these models.

Findings

Identification of conditions for accelerated expansion

Existence of finite-time singularities as attractors

Instability linked to higher-order derivatives in field equations

Abstract

We investigate the evolution of non vacuum Friedmann-Lema\^itre-Robertson-Walker (FLRW) with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the the emergence of accelerated expansion. As in $f(R)$ gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.