Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term

TL;DR

This paper investigates the cosmological behavior of a modified gravity model combining $f(R)$ and Gauss-Bonnet corrections, analyzing the stability of solutions including de Sitter space using dynamical systems.

Contribution

It provides a comprehensive analysis of the stability conditions for power-law and de Sitter solutions in fourth order gravity with combined $f(R)$ and Gauss-Bonnet terms.

Findings

Power-law solutions where both corrections are significant are identified.

Stability conditions for de Sitter solutions are derived.

The dynamical system approach reveals the parameter regimes for stable cosmological evolution.

Abstract

We consider cosmological dynamics in fourth order gravity with both $f(R)$ and $\Phi(\mathcal {G})$ correction to the Einstein gravity ($\mathcal{G}$ is the Gauss-Bonnet term). The particular case for which both terms are equally important on power-law solutions is described. These solutions and their stability are studied using the dynamical system approach. We also discuss condition of existence and stability of de Sitter solution in a more general situation of power-law $f$ and $\Phi$.