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 ({OMEGA} = 1) are inconsistent with these observations for any bias parameter b. A low-density, low-bias ({OMEGA} ~ 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 {DELTA} = 1 - {OMEGA}, with the COBE results of the microwave background radiation fluctuations.
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Bahcall et al. (1992) studied this question.