We study the ability of COBE-normalized cold dark matter (CDM) models to reproduce observed properties of the distribution of galaxies and clusters using N-body numerical simulations. We analyze the galaxy-galaxy and cluster-galaxy two-point correlation functions, ξ_gg and ξ_cg, in open (Ω₀ = 0.4, Ω_Λ = 0, σ₈ = 0.75) and flat (Ω₀ = 0.3, Ω_Λ = 0.7, σ₈ = 1.05) CDM models, both of which reproduce the observed abundances of rich clusters of galaxies.

To compare models with observations, we compute projected cross-correlation functions ω_gg and ω_cg to derive the corresponding ξ_gg and ξ_cg. We use target galaxies selected from the Las Campanas Redshift Survey, target clusters selected from the APM Cluster Survey, and tracer galaxies from the Edinburgh Durham Sky Survey catalog.

We find that the open model is able to reproduce the observed ξ_gg, whereas the flat model needs antibias in order to fit the observations. Our estimate of ξ_cg for the APM cluster sample analyzed is consistent with a power law ξ_cg = (r/r₀)^γ with r₀ = 10.0 ± 0.7 h^-1 Mpc and γ -2.1. For the open and flat-antibiased CDM models explored we find the corresponding cluster-galaxy correlation lengths 6.5 ± 0.7 h^-1 Mpc and 7.2 ± 0.5 h^-1 Mpc, respectively, significantly lower than the observed value. Our results indicate that COBE-normalized CDM models are not able to reproduce the spatial cross-correlation of clusters and galaxies.