Large-scale structure in COBE-normalized cold dark matter cosmogonies

We study the clustering of the mass distribution in cold dark matter models using large cosmological N-body simulations. We investigate spatially flat models with a cosmological constant and scale-invariant (n = 1) primordial power spectra, as well as open-bubble inflation models. All the models we consider are normalized according to the fluctuation amplitude measured in the COBE-DMR microwave background anisotropy data, With an age of the universe t(0) approximate to 14 Gyr (12 Gyr) for the hat (open) models, a baryon mass density parameter Omega(B) = 0.0125 h(-2), and a reasonable assessment of the systematic uncertainties in the cumulative cluster mass function, the observed abundance of rich galaxy clusters leads to tight constraints on the mass density parameter Omega(0). The allowable ranges are 0.4 less than or similar to Omega(0) less than or similar to 0.5 for open models and 0.25 less than or similar to Omega(0) less than or similar to 0.4 for flat models, The upper limits on Omega(0) can be relaxed if one lowers the Hubble parameter and increases the age of the universe, but h less than or similar to 0.25 is required for Omega(0) = 1 to be allowed. The constraints also change if one allows tilted primordial power spectra. An Omega(0) = 1 cold dark matter model with h = 0.5 can be constructed to satisfy both the cluster and DMR constraints, but it requires a tilted primordial power spectrum with n approximate to 0.8 and a corresponding contribution to the DMR signal from gravitational waves that reduces thr implied sigma(8) by a further 27 per cent. We compare the evolved mass correlation functions and power spectra of the most promising of our N-body models with those of galaxies in the APM survey. The flat models have steep correlation functions at small scales and require the galaxy distribution to be antibiased on scales r less than or similar to 8 h(-1) Mpc. The open models require little or no antibias on small scales and a positive bias on large scales; these biases are small for Omega(0) approximate to 0.4, implying that, in this case, galaxies approximately trace the mass over a wide range of scales, The lack of a positive bias on small scales in almost all of these N-body models is difficult to reconcile with the mean mass-to-light ratio of cluster galaxies which, if Omega(0) greater than or similar to 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 small scales, and that the bias become stronger on larger scales. We also compute the topology of isodensity contours in these models, obtaining theoretical predictions that are less sensitive to the details of galaxy formation.