Finite-time future singularities in modified Gauss-Bonnet and $\mathcal{F}(R,G)$ gravity and singularity avoidance

TL;DR

This paper investigates finite-time future singularities in modified Gauss-Bonnet and (R,G) gravity theories, reconstructs models with such singularities, and proposes higher-order curvature corrections to avoid these singularities.

Contribution

It provides a comprehensive analysis of future singularities in (R,G) gravity and introduces methods to cure them using higher-order curvature corrections.

Findings

Finite-time singularities can be realized in (R,G) gravity models.

Higher-order curvature corrections can effectively remove or avoid these singularities.

Non-singular modified Gauss-Bonnet gravity models are constructed and shown to be stable.

Abstract

We study all four types of finite-time future singularities emerging in late-time accelerating (effective quintessence/phantom) era from $\mathcal{F}(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of $\mathcal{F}(R,G)$-gravity, we also investigate modified Gauss-Bonnet gravity, so-called $F(G)$-gravity. In particular, we reconstruct the $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory to be non-singular one as well.