Spherical collapse in generalized dark matter models

F Pace,I Tutusaus,Z Sakr

doi:10.1103/physrevd.102.043512

Abstract

The influence of considering a generalized dark matter (GDM) model, which allows for a non-pressure-less dark matter and a non-vanishing sound speed in the non-linear spherical collapse model is discussed for the Einstein-de Sitter-like (EdSGDM) and $\Lambda$GDM models. By assuming that the vacuum component responsible for the accelerated expansion of the Universe is not clustering and therefore behaving similarly to the cosmological constant $\Lambda$, we show how the change in the GDM characteristic parameters affects the linear density threshold for collapse of the non-relativistic component ($\delta_{\rm c}$) and its virial overdensity ($\Delta_{\rm V}$). We found that the generalized dark matter equation of state parameter $w_{\rm gdm}$ is responsible for lower values of the linear overdensity parameter as compared to the standard spherical collapse model and that this effect is much stronger than the one induced by a change in the generalized dark matter sound speed $c^2_{\rm s, gdm}$. We also found that the virial overdensity is only slightly affected and mostly sensitive to the generalized dark matter equation of state parameter $w_{\rm gdm}$. These effects could be relatively enhanced for lower values of the matter density. Finally, we found that the effects of the additional physics on $\delta_{\rm c}$ and $\Delta_{\rm V}$, when translated to non-linear observables such as the halo mass function, induce an overall deviation of about 40\% with respect to the standard $\Lambda$CDM model at late times for high mass objects. However, within the current linear constraints for $c^2_{\rm s, gdm}$ and $w_{\rm gdm}$, we found that these changes are the consequence of properly taking into account the correct linear matter power spectrum for the GDM model while the effects coming from modifications in the spherical collapse model remain negligible.

Highlights

With the advent of stage IV surveys like DESI [4], Euclid [5], LSST [6], WFIRST [7], and the SKA [8] providing high accuracy data especially on small scales, one of the most challenging problems is to understand the role played by the different cosmic components in the nonlinear regime of gravitational clustering
We present some results for the spherical collapse model for the generalized dark matter models previously discussed, taking into account the effects of both the background equation-of-state parameter wgdm and the effective sound speed c2s;gdm
These quantities have both their own theoretical importance: the linear overdensity parameter is a key ingredient for the halo mass function, while the virial overdensity is a measure of how dense cosmic structures are and in first approximation, assuming spherical symmetry, it gives a measure of their radius knowing their mass

Summary

INTRODUCTION

With the advent of stage IV surveys like DESI [4], Euclid [5], LSST [6], WFIRST [7], and the SKA [8] providing high accuracy data especially on small scales, one of the most challenging problems is to understand the role played by the different cosmic components in the nonlinear regime of gravitational clustering This aspect could be tackled through different approaches, among which we recall the halo model [9], where one of the issues is to understand the interplay of different possible.

THE GDM MODEL

RESULTS

The mass function

Comparison with observations

The nonlinear matter power spectrum

CONCLUSIONS