Spherical collapse model with shear and angular momentum in dark energy cosmologies

We study, for the first time, how shear and angular momentum modify typical parameters of the spherical collapse model, in dark energy dominated universes. In particular, we study the linear density threshold for collapse $\delta_\mathrm{c}$ and the virial overdensity $\Delta_\mathrm{V}$, for several dark-energy models and its influence on the cumulative mass function. The equations of the spherical collapse are those obtained in Pace et al. (2010), who used the fully nonlinear differential equation for the evolution of the density contrast derived from Newtonian hydrodynamics, and assumed that dark energy is present only at the background level. With the introduction of the shear and rotation terms, the parameters of the spherical collapse model are now mass-dependant. The results of the paper show, as expected, that the new terms considered in the spherical collapse model oppose the collapse of perturbations on galactic scale giving rise to higher values of the linear overdensity parameter with respect to the non-rotating case. We find a similar effect also for the virial overdensity parameter. For what concerns the mass function, we find that its high mass tail is suppressed, while the low mass tail is slightly affected except in some cases, e.g. the Chaplygin gas case.