THE CORRELATION-FUNCTION OF RICH CLUSTERS OF GALAXIES IN CDM-LIKE MODELS

We use ensembles of high-resolution CDM simulations to investigate the shape and amplitude of the two-point correlation function of rich clu sters. The standard scale-invariant CDM model with OMEGA = 1 provides a poor description of the clustering measured from the APM rich cluste r redshift survey, which is better fitted by models with more power at large scales. The amplitudes of the rich cluster correlation function s measured from our models depend weakly on cluster richness. Analytic calculations of the clustering of peaks in a Gaussian density field o verestimate the amplitude of the N-body cluster correlation functions, but reproduce qualitatively the weak trend with cluster richness. Our results suggest that the high amplitude measured for the correlation function of richness class R greater-than-or-equal-to 2 Abell clusters is either an artefact arising from incompleteness in the Abell catalo gue, or an indication that the density perturbations in the early Univ erse were very non-Gaussian.