Structure Formation in Gauss-Bonnet Gravity

Abstract

We explore the influences of the higher order Gauss-Bonnet (GB) correction terms on the growth of perturbations at the early stage of the universe. We consider a Friedmann-Robertson-Walker (FRW) background in the presence a cosmological constant, and study the linear perturbations by adopting the spherically symmetric collapse (SC) formalism. We disclose the role of the GB coupling parameter α, as well as the extra dimension on the growth of perturbations. We find that the matter density contrast starts growing at the early stages of the universe and, as the universe expands, it grows faster compared to the Einstein gravity. Besides, in the framework of GB gravity, the growth of matter perturbations in higher dimensions is faster than four-dimensions. Further, the growth of perturbations increases with increasing the GB coupling parameter α. This is an expected result, since the higher order GB correction terms increase the strength of the gravity and thus support the growth of perturbations. Finally, we explore the behavior of the density abundance, the deceleration parameter and jerk parameter of this model.