Large - scale structure in COBE - normalized cold darkmatter

We study the clustering of the mass distribution in cold dark matter models using large cosmological N-body simulations. We investigate spatially-at models with a cosmological constant and scale-invariant (n = 1) primordial power spectra, as well as open-bubble innation models. All the models we consider are normalized according to the uctuation amplitude measured in the COBE-DMR microwave background anisotropy data. With an age of the universe t 0 14 Gyr (12 Gyr) for the at (open) models, a baryon mass density parameter B = 0:0125h ?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 0. The allowable ranges are 0:4 < 0 < 0:5 for open models and 0:25 < 0 < 0:4 for at models. The upper limits on 0 can be relaxed if one lowers the Hubble pararameter and increases the age of the universe, but h < 0:25 is required for 0 = 1 to be allowed. The constraints also change if one allows tilted primordial power spectra. An 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 0:8 and a corresponding contribution to the DMR signal from gravitational waves that reduces the implied 8 by a further 27%. 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 at models have steep correlation functions at small scales and require the galaxy distribution to be antibiased on scales r < 8h ?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 ' 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 diicult to reconcile with the mean mass-to-light ratio of cluster galaxies which, if 0 > 0:2, implies that galaxies are overabundant in clusters relative to the eld. The tilted 0 = 1 model, on the other hand, does require that galaxies be positively biased on small scales, and that the bias to become …