$f(R,\mathcal{G})$-cosmological dynamics in the FLRW background

TL;DR

This paper studies a modified gravity model combining Ricci scalar and Gauss-Bonnet term in a flat FLRW universe, showing it can unify early and late cosmic acceleration and analyzing its stability and cosmological implications.

Contribution

It introduces a specific $f(R+ ext{Gauss-Bonnet})$ model, analyzes its phase space, stability, and demonstrates its potential to unify inflation and dark energy epochs.

Findings

The model exhibits double inflationary epochs.

Stable de Sitter solutions are identified.

The theory can incorporate cold dark matter effects.

Abstract

We examine the cosmological dynamics of Einstein-Gauss-Bonnet gravity models in a four-dimensional spatially flat FLRW metric. These models are described by $f\left( R,\mathcal{G}\right) =f\left( R+\mu \mathcal{G}\right) $ theory of gravity. They are equivalent to models linear in the Ricci scalar $R$ and in the Gauss-Bonnet scalar $\mathcal{G}$ with one nonminimally coupled scalar field without kinetic term. We analyze the stability of the de Sitter solutions and construct the phase space of the field equations to investigate the cosmological evolution. We show that $f\left( R+\mu \mathcal{G}\right) $-theory provides a double inflationary epoch, this can be used to unify the early-time and late-time acceleration phases of the universe. Moreover, we discuss the initial value problem for theory to be cosmologically viable. Finally, the effects of the cold dark matter in cosmic evolution are discussed.