Spherical collapse in generalized dark matter models

The influence of considering a generalized dark matter (GDM) model, which allows for a non-pressure-less dark matter and a nonvanishing sound speed in the nonlinear spherical collapse model is discussed for the Einstein-de Sitter-like and ΛGDM 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 Λ, we show how the change in the GDM characteristic parameters affects the linear density threshold for collapse of the nonrelativistic component (δc) and its virial overdensity (ΔV). We found that a positive GDM equation of state parameter, wgdm, is responsible for lower values of δc as compared to the standard spherical collapse model and that this effect is much stronger than the one induced by a change in the GDM sound speed, cs,gdm2. We also found that ΔV is only slightly affected and mostly sensitive to wgdm. These effects could be relatively enhanced for lower values of the matter density. We found that the effects of the additional physics on δc and ΔV, when translated to nonlinear observables such as the halo mass function, induce an overall deviation of about 40% with respect to the standard ΛCDM model at late times for high mass objects. However, within the current constraints for cs,gdm2 and wgdm, 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. Using a phenomenologically motivated approach, we also study the nonlinear matter power spectrum and found that the additional properties of the dark matter component lead, in general, to a strong suppression of the nonlinear power spectrum with respect to the corresponding ΛCDM one. Finally, as a practical example, we compare ΛGDM and ΛCDM using galaxy cluster abundance measurements, and found that these small scale probes will allow us to put more stringent constraints on the nature of dark matter.