Determining Omega from the cluster correlation function

It is shown how data on the cluster correlation function can be used to rec onstruct the density of the pregalactic density field on the cluster mass s cale. The method is applied to data on the cluster correlation amplitude-ri chness dependence. The spectrum of the recovered density field has the same shape as that derived from data on the galaxy correlation function is meas ured as a function of a linear scale. Matching the two amplitudes relates t he mass to the comoving scale it contains and thereby leads to a direct det ermination of Omega. The resultant density parameter turns out to be Omega = 0.25. (C) 1998 Elsevier Science B.V. All rights reserved.