Galaxy clusters and cold dark matter: A low-density unbiased universe?

Large-scale (L = 400 h^-1 Mpc) simulations of a universe dominated by cold dark matter (CDM) are tested against two fundamental properties of clusters of galaxies: the cluster mass function and the cluster correlation function. We find that standard biased CDM models (Ω = 1) are inconsistent with these observations for any bias parameter b. A low-density, low-bias (Ω ∼ 0.25, b ∼ 1) CDM-type model, with or without a cosmological constant, appears to be consistent with both the cluster mass function and the cluster correlations. The low-density model agrees well with the observed correlation function of the Abell, Automatic Plate Measuring Facility (APM), and Edinburgh-Durham cluster catalogs. The model is in excellent agreement with the observed dependence of the correlation strength on cluster mean separation, reproducing the measured universal dimensionless cluster correlation, ξ_cc = 0.2(r/d)^-1.8. The low-density model is also consistent with other large-scale structure observations, including the APM angular galaxy correlations, and for Λ = 1 - Ω, with the COBE results of the microwave background radiation fluctuations.