We study the clustering of the mass distribution in COBE-normalized open and flat CDM models using large N-body simulations. With an age of the universe of 14 Gyr (12 Gyr) for the flat (open) models and a baryon density fixed by nucleosynthesis constraints, the observed abundance of rich galaxy clusters leads to tight constraints on the density parameter; 0.25<Omega_0<0.4 (0.4<Omega_0<0.5) for flat (open) models. The upper limits on Omega_0 can be relaxed if one lowers the H_0 and increases the age of the universe, but h<0.25 is required to allow Omega_0=1. The constraints also change if one allows tilted primordial power spectra. An acceptable Omega_0=1 model with h=0.5 can be constructed, with a tilt of n=0.8. We compare the evolved mass correlation functions of the most promising models with those of APM galaxies. The flat models have steep correlation functions at small scales and require galaxies to be antibiased on scales r<8 Mpc/h. The open models require little or no antibias on small scales and a positive bias on large scales. The lack of a positive bias on small scales is difficult to reconcile with the virial analysis of galaxy clusters which, if Omega_0>0.2, implies that galaxies are overabundant in clusters relative to the field. The tilted Omega_0=1 model, on the other hand, does require that galaxies be positively biased on all scales. We also compute the topology of isodensity contours in these models, obtaining theoretical predictions that are less sensitive to galaxy bias.
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