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 ($Γ$), the spectral index ($n$), the amplitude of matter density perturbations on the scale of $8 h^{-1}$Mpc ($σ_8$), and the redshift distortion parameter ($β$). The non-spherical-collapse model as an improvement to the Press-Schechter formula is used and yields significantly lower $σ_8$ and $β$. An analytical formalism for the formation redshift of halos is also derived.

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