Evolution of the cluster correlation function

We study the evolution of the cluster correlation function and its richness dependence from z=0 to z=3 using large-scale cosmological simulations. A standard flat LCDM model with Omega(m)=0.3 and, for comparison, a tilted Omega(m)=1 model (TSCDM) are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high-redshift clusters are clustered more strongly (on a comoving scale) than low-redshift clusters of the same mass. The increased correlation with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation scale versus cluster mean separation relation, R-0-d, is found to be, remarkably, independent of redshift to zless than or similar to2 for LCDM and zless than or similar to1 for TSCDM for a fixed correlation function slope and a cluster mass within a fixed comoving radius. The nonevolving R-0-d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters, so that the R-0-d relation remains essentially unchanged. For LCDM, this relation is R-0(z)similar or equal to 2.6 [d(z)](1/2) for zless than or similar to2 in comoving h(-1) Mpc scales. The TSCDM model has smaller correlation scales, as expected. Evolution in the relation is seen at zgreater than or similar to2 for LCDM and zgreater than or similar to1 for TSCDM, where the amplitude of the relations declines. The evolution of the R-0-d relation from zsimilar to0 to zsimilar to3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at zsimilar to0 and provide precise determination of cosmological parameters.