Determining $\Omega$ from cluster correlation function

Abstract

It is shown how data on the cluster correlation function can be used in order to reconstruct the density of the pregalactic density field on the cluster mass scale. The method is applied to the data on the cluster correlation amplitude -- richness dependence. The spectrum of the recovered density field has the same shape as the density field derived from data on the galaxy correlation function which is measured as function of linear scales. Matching the two amplitudes relates the mass to the comoving scale it contains and thereby leads to a direct determination of $\Omega$. The resultant density parameter turns out to be $\Omega$=0.25.