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 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 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.