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

Abstract

We study finite-time future singularities in $\mathcal{F}(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. In particular, we reconstruct the $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity models realizing the finite-time future singularities. We discuss a possible way to cure the finite-time future singularities in $\mathcal{F}(R,G)$-gravity by taking into account higher-order curvature corrections or effects of viscous fluids.

10 pages, submitted to the volume "Cosmology, Quantum Vacuum, and Zeta Functions", in honour of Professor Emilio Elizalde on the occasion of his 60th birthday