Constraining cosmological models with cluster power spectra

Using extensive N-body simulations we estimate redshift space power spectra of clusters of galaxies for different cosmological models (SCDM, TCDM, CHDM, Lambda-CDM, OCDM, BSI, tau-CDM) and compare the results with observational data for Abell-ACO clusters. Our mock samples of galaxy clusters have the same geometry and selection functions as the observational sample which contains 417 clusters of galaxies in a double cone of galactic latitude |b| > 30 degrees up to a depth of 240 Mpc/h. The power spectrum has been estimated for wave numbers k in the range 0.03 < k < 0.2 h/Mpc. For k > k_max ~ 0.05 h/Mpc the power spectrum of the Abell-ACO clusters has a power-law shape, P(k)\propto k^n, with n ~ -1.9, while it changes sharply to a positive slope at k < k_max. By comparison with the mock catalogues SCDM, TCDM (n=0.9), and also OCDM with Omega_0 = 0.35 are rejected. Better agreement with observation can be found for the Lambda-CDM model with Omega_0 = 0.35 and h = 0.7 and the CHDM model with two degenerate neutrinos and Omega_HDM = 0.2 as well as for a CDM model with broken scale invariance (BSI) and the tau-CDM model. As for the peak in the Abell-ACO cluster power spectrum, we find that it does not represent a very unusual finding within the set of mock samples extracted from our simulations.