Improvements in the Spherical Collapse Model and Dark Energy Cosmologies

Abstract

Abstract In the present paper, we study how the effects of deviations from spherical symmetry of a system, produced by angular momentum, and shear stress, influence typical parameters of the spherical collapse model, like the linear density threshold for collapse of the non-relativistic component (δ c) and its virial overdensity (ΔV). The study is performed in the framework of the Einstein-de Sitter and ΛCDM models, and assuming that the vacuum component is not clustering within the homogeneous non-spherical overdensities. We start from the standard spherical top hat model (SCM) which does not take account the non-spherical effects, and we add to this model the shear term and angular momentum term, which are finally expressed in terms of the density contrast, δ. We find that the non-spherical terms change the non-linear evolution of the system and that the collapse stops “naturally” at the virial radius, differently from the standard spherical collapse model. Moreover, shear and rotation gives rise to higher values of the linear overdensity parameter and different values of ΔV with respect to the standard spherical collapse model.