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

TL;DR

This paper investigates the growth of dark matter perturbations in a clustering DBI dark energy model with constant sound speed, analyzing both linear and non-linear regimes and comparing clustering versus homogeneous scenarios.

Contribution

It introduces a clustering DBI dark energy model with constant sound speed and studies its impact on structure formation using both linear and non-linear analyses.

Findings

Smaller sound speed leads to reduced dark matter growth factor.

Clustering DBI models show more deviation from mbda CDM than homogeneous models.

Differences are more significant for high-mass halos at high redshift.

Abstract

Within the framework of DBI non-canonical scalar field model of dark energy, we study the growth of dark matter perturbations in the both 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 $f_0>0$ and assume the DBI dark energy to be clustered and its sound speed $c_s$ to be constant. For a spatially flat FRW universe filled with pressureless dark matter and DBI dark energy, we first obtain the evolutionary behaviors of the background quantities. Our results show that in our DBI model, the universe starts from a matter dominated epoch and approaches to the de Sitter universe at late times, as expected. Also the DBI potential behaves like the power law one $V(\phi)\propto \phi^n$. In addition, we use the Pseudo-Newtonian formalism to obtain the growth factor of dark matter perturbations in the linear regime. We conclude that for smaller $c_s$ (or $f_0$), the growth factor of dark matter is smaller for clustering DBI model compared to the homogeneous one. In the following, in the non-linear regime based on the spherical collapse model, we obtain the linear overdensity $\delta_c(z_c)$, the virial overdensity $\Delta_{\rm vir}(z_c)$, overdensity at the turn around $\zeta(z_c)$ and the rate of expansion of collapsed region $h_{\rm ta}(z)$. We point out that for the smaller $c_s$ (or $\tilde{f}_0$), the values of $\delta_c(z_c)$, $\Delta_{\rm vir}(z_c)$, $\zeta(z_c)$ and $h_{\rm ta}(z)$ in non-clustering DBI models deviate more than the $\Lambda$CDM compared to the clustering DBI. Finally, with the help of spherical collapse parameters we calculated 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 higher-mass halos at high redshift.