Structure formation in clustering DBI dark energy model with constant sound speed

Abstract

ABSTRACT Within the framework of DBI non-canonical scalar field model of dark energy, we study the growth of dark matter perturbations in both the linear and non-linear regimes. In our DBI model, we consider the anti-de Sitter warp factor $f(\phi)=f_0\, \phi ^{-4}$ with constant f0 > 0 and assume the DBI dark energy to be clustered and its sound speed cs to be constant. In the linear regime, we use the pseudo-Newtonian formalism to obtain the growth factor of dark matter perturbations and conclude that for smaller cs (or $\tilde{f_0} \equiv f_0 H_0^2/M_P^2$), the growth factor of dark matter is smaller for clustering DBI model compared to the homogeneous one. In the non-linear regime based on the spherical collapse model, we obtain the linear overdensity δc($z$c), the virial overdensity Δvir($z$c), overdensity at the turn around ζ($z$c), and the rate of expansion of collapsed region hta($z$). We point out that for the smaller cs (or $\tilde{f_0}$), the values of δc($z$c), Δvir($z$c), ζ($z$c), and hta($z$) in non-clustering DBI models deviate more than the ΛCDM compared to the clustering DBI models. Finally, with the help of spherical collapse parameters we calculate the relative number density of halo objects above a given mass and conclude that the differences between clustering and homogeneous DBI models are more pronounced for the higher mass haloes at high redshift.