Dynamical analysis on $f(R,\mathcal{G})$ cosmology

TL;DR

This paper employs a dynamical systems approach to analyze the cosmological behavior of $f(R, ext{G})$ gravity models, identifying new accelerating solutions but also highlighting their inconsistency with matter-dominated epochs.

Contribution

It introduces a dynamical system formulation for $f(R, ext{G})$ gravity and analyzes a specific class of models, revealing new accelerating attractors and their limitations.

Findings

Discovery of new accelerating attractor solutions.

Identification that the models lack a matter-dominated epoch.

Analysis of stability properties of solutions.

Abstract

We use a dynamical system approach to study the cosmological viability of $f(R,\mathcal{G})$ gravity theories. The method consists of formulating the evolution equations as an autonomous system of ODEs, using suitable variables. The formalism is applied to a class of models in which $f(R,\mathcal{G})\propto R^{n}\mathcal{G}^{1-n}$ and its solutions and corresponding stability are analysed in detail. New accelerating solutions that can be attractors in the phase space are found. We also find that this class of models does not exhibit a matter-dominated epoch, a solution which is inconsistent with current cosmological observations.