Two cosmological models for clusters of galaxies

We investigate the properties of clusters of galaxies in two cosmological models using N-body simulations and the Press-Schecter (PS) theory. In the first model, the initial power spectrum of density fluctuations is in the form P(k) \\propto k^{-2} at wavelengths \\lambda<120h^{-1} Mpc. In the second model, the initial linear power spectrum of density fluctuations contains a feature (bump) at wavelengths \\lambda \\sim 30-60h^{-1} Mpc which correspond to the scale of superclusters of galaxies. We examine the mass function, peculiar velocities, the power spectrum and the correlation function of clusters in both models for different values of the density parameter Ømega_0 and \\sigma_8. The results are compared with observations. We show that in many aspects the second model fits the observed data better than the first simple power law model. We examine the linear theory predictions for the peculiar velocities of peaks in the Gaussian field and compare these to the peculiar velocities of clusters in N-body simulations. The numerical results show that the rms peculiar velocity of clusters increases with cluster richness. The rms peculiar velocity of small clusters is similar to the linear theory expectations, while the rms peculiar velocity of rich clusters is higher than that predicted in the linear theory (\\sim 17% for clusters with a mean intercluster separation d_{cl} \\sim 30h^{-1} Mpc).