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

Kazuharu Bamba, Sergei D. Odintsov, Lorenzo Sebastiani, Sergio Zerbini
2010 European Physical Journal C: Particles and Fields  
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
more » ... rating 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.
doi:10.1140/epjc/s10052-010-1292-8 fatcat:dvqvwrsdwrcvnp7au4d6gnrcty