Cluster abundance and large-scale structure

We use the presently observed number density of large X-ray clusters and linear mass power spectra to constrain the shape parameter ($Gamma$), the spectral index ($n$), the amplitude of matter density perturbations on the scale of $8 h^{-1}$Mpc ($sigma_8$), and the redshift distortion parameter ($beta$). The non-spherical-collapse model as an improvement to the Press-Schechter formula is used and yields significantly lower $sigma_8$ and $beta$. An analytical formalism for the formation redshift of halos is also derived.