Gauss-Bonnet modified gravity models with bouncing behavior

The following issue is addressed: how the addition of a Gauss-Bonnet term (generically coming from most fundamental theories, as string and M theories), to a viable model, can change the specific properties, and even the physical nature, of the corresponding cosmological solutions? Specifically, brand new original dark energy models are obtained in this way with quite interesting properties, which exhibit, in a unified fashion, the three distinguished possible cosmological phases corresponding to phantom matter, quintessence, and ordinary matter, respectively. A model, in which the equation of state parameter, $w$, is a function of time, is seen to lead either to a singularity of the Big Rip kind or to a bouncing solution which evolves into a de Sitter universe with $w=-1$. Moreover, new Gauss-Bonnet modified gravity models with bouncing behavior in the early stages of the universe evolution are obtained and tested for the validity and stability of the corresponding solutions. They allow for a remarkably natural, unified description of a bouncing behavior at early times and accelerated expansion at present.