Finite-time future singularities in modified Gauss–Bonnet and ℱ(R,G) gravity and singularity avoidance

Abstract

We study all four types of finite-time future singularities emerging in the late-time accelerating (effective quintessence/phantom) era from ℱ(R,G)-gravity, where R and G are the Ricci scalar and the Gauss–Bonnet invariant, respectively. As an explicit example of 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 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 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 a non-singular one as well.