Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity

We study how a cosmological bounce with a Type IV singularity at the bouncing point, can be generated by a classical vacuum $F(G)$ gravity. We focus our investigation on the behavior of the vacuum $F(G)$ theory near the Type IV singular bouncing point and also we address the stability of the resulting solution, by treating the equations of motion as a dynamical system. In addition, we investigate how the scalar perturbations of the background metric evolve, emphasizing to cosmological times near the Type IV singular bouncing point. Finally, we also investigate which mimetic vacuum $F(G)$ gravity can describe the singular bounce cosmology.