Growth of perturbations in higher dimensional Gauss-Bonnet FRW cosmology

Abstract

We explore the influences of the higher order Gauss Bonnet (GB) correction terms on the growth of perturbations at the early stage of a (n + 1)-dimensional Friedmann-Robertson-Walker (FRW) universe. Considering a cosmological constant in the FRW background, we study the linear perturbations by adopting the spherically symmetric collapse (SC) formalism. In light of the modifications that appear in the field equations, we disclose the role of the GB coupling constant {\alpha}, as well as the extra dimensions n > 3 on the growth of perturbations. It, in essence, is done by defining a dimensionless parameter \{beta}=(n-2)(n-3) \{alpha} H_0^2 in which H_0 is the Hubble constant. 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 standard cosmology. Besides, in the framework of GB gravity, the growth of matter perturbations in higher dimensions is faster than its standard counterpart (n = 3). Further, in the presence of {\alpha}, the growth of perturbations increases as it increases. 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. For the existing cosmological model, we also investigate the behavior of quantities such as density abundance, deceleration, and the jerk parameter. Finally, we study the imprint of the GB parameter and the higher dimensions in the evolution of the mass function of the dark matter halos.