The correlation function of rich clusters of galaxies in CDM-like models

We use ensembles of high-resolution CDM simulations to investigate the shapeand amplitude of the two point correlation function of rich clusters. Thestandard scale-invariant CDM model with $\Omega=1$ provides a poor descriptionof the clustering measured from the APM rich cluster redshift survey, which isbetter fitted by models with more power at large scales. The amplitudes of therich cluster correlation functions measured from our models depend weakly oncluster richness. Analytic calculations of the clustering of peaks in aGaussian density field overestimate the amplitude of the N-body clustercorrelation functions, but reproduce qualitatively the weak trend with clusterrichness. Our results suggest that the high amplitude measured for thecorrelation function of richness class $R \geq 2$ Abell clusters is either anartefact arising from incompleteness in the Abell catalogue, or an indicationthat the density perturbations in the early universe were very non-Gaussian.Comment: uuencoded compressed postscript ,MNRAS, in press, OUAST-93-1