Dynamical systems of modified Gauss-Bonnet gravity: cosmological implications

TL;DR

This paper investigates the cosmological dynamics of modified Gauss-Bonnet gravity models using a dynamical systems approach, analyzing stability and evolution of the universe with different functional forms of the gravity modification.

Contribution

It introduces a dynamical systems framework to analyze specific $f(R,G)$ gravity models and explores their cosmological implications and stability properties.

Findings

Existence of fixed points for late-time acceleration and radiation phases.

Dependence of matter-dominated fixed points on the functional form of $f(R,G)$.

Qualitative evolution of the universe varies with different $f(R,G)$ models.

Abstract

In this paper, we derive the field equations of modified Gauss-Bonnet gravity termed as $f(R,G)$ gravity for the non-flat Friedmann-Robertson-Walker (FRW) spacetime. We utilize the dynamical system approach to study the cosmic dynamics of two different class of $f(R,G)$ models composed of radiation and matter (cold dark matter and baryonic matter). The linear perturbations around the fixed points are studied to explore the corresponding stability of points. The cosmological implications are studied in $f(R,G)=f_0R^nG^{1-n}$ and $f(R,G)=f_0R^\alpha+f_1G^\beta$ models to identify the qualitative evolution of universe with the flat-FRW spacetime. The qualitative differences between the considered class of models are discussed in detail. The fixed points corresponding to the late-time accelerated and radiation phase of the universe will exist in the model but, the existence of fixed point corresponding to the matter dominated phase will depend on the functional form of $f(R,G)$. Furthermore, the autonomous systems are utilized to study the cosmographic parameters along with the statefinder diagnostic.