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

We study all four types of finite-time future singularities emerging in 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 to be non-singular one as well. PACS numbers: 04.50.Kd, 11.25.-w, 95.36.+x, 98.80.-k ∗ E-mail address: [email protected] † Also at Tomsk State Pedagogical University. E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected] 1