Evolution of the Cluster Mass and Correlation Functions in a ΛCDM Cosmology

The evolution of the cluster mass function and the cluster correlationfunction from z = 0 to z = 3 are determined using 10^6 clusters obtained fromhigh-resolution simulations of the current best-fit LCDM cosmology (\Omega_m =0.27, \sigma_8 = 0.84, h = 0.7). The results provide predictions forcomparisons with future observations of high redshift clusters. A comparison ofthe predicted mass function of low redshift clusters with observations fromearly Sloan Digital Sky Survey data, and the predicted abundance of massivedistant clusters with observational results, favor a slightly larger amplitudeof mass fluctuations (\sigma_8 = 0.9) and lower density parameter (\Omega_m =0.2); these values are consistent within 1-\sigma with the currentobservational and model uncertainties. The cluster correlation functionstrength increases with redshift for a given mass limit; the clusters were morestrongly correlated in the past, due to their increasing bias with redshift -the bias reaches b = 100 at z = 2 for M > 5 x 10^13 h^-1 M_sun. Therichness-dependent cluster correlation function, represented by the correlationscale versus cluster mean separation relation, R0-d, is generally consistentwith observations. This relation can be approximated as R_0 = 1.7 d^0.6 h^-1Mpc for d = 20 - 60 h^-1 Mpc. The R0-d relation exhibits surprisingly littleevolution with redshift for z < 2; this can provide a new test of the currentLCDM model when compared with future observations of high redshift clusters.Comment: 20 pages, 9 figures, accepted for publication in Ap