On the Abundance of Collapsed Objects

The redshift dependence of the abundance of collapsed objects places strong constraints on cosmological models of structure formation. We apply a recently proposed model describing the anisotropic collapse of inhomogeneous spatial domains. Compared with the spherical top-hat model, this generic model leads to significantly more collapsed objects at high redshifts: at redshift 1 and on the scale of rich clusters a factor of 65. Furthermore, for a fixed normalization of the initial fluctuation spectrum (σ₈=1), we predict 4 times as much presently collapsed objects on the mass scale of rich clusters within the standard cold dark matter cosmogony compared to the spherical collapse.