Cosmological scaling solutions in generalised Gauss-Bonnet gravity theories

TL;DR

This paper investigates the conditions under which modified gravity theories involving the Gauss-Bonnet term can produce stable, power-law cosmological scaling solutions, providing a systematic analysis of their existence and stability.

Contribution

It determines the general form of the Gauss-Bonnet function that admits stable scaling solutions and analyzes their stability using an autonomous system approach.

Findings

Stable scaling solutions exist for specific parameter ranges.

The Gauss-Bonnet modified gravity can be recast as a scalar-tensor theory.

Conditions for the existence and stability of solutions are established.

Abstract

The conditions for the existence and stability of cosmological power-law scaling solutions are established when the Einstein-Hilbert action is modified by the inclusion of a function of the Gauss-Bonnet curvature invariant. The general form of the action that leads to such solutions is determined for the case where the universe is sourced by a barotropic perfect fluid. It is shown by employing an equivalence between the Gauss-Bonnet action and a scalar-tensor theory of gravity that the cosmological field equations can be written as a plane autonomous system. It is found that stable scaling solutions exist when the parameters of the model take appropriate values.