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, ΛCDM, OCDM, BSI, τCDM) 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° up to a depth of 240 h^-1 Mpc. The power spectrum has been estimated for wave numbers k in the range 0.03≲k≲0.2 h Mpc^-1. For k>k_max≃0.05 h Mpc^-1 the power spectrum of the Abell-ACO clusters has a power-law shape, P(k)∝kⁿ, 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 Ω₀=0.35 are rejected. Better agreement with observation can be found for the ΛCDM model with Ω₀=0.35 and h=0.7 and the CHDM model with two degenerate neutrinos and Ω_HDM=0.2 as well as for a CDM model with broken scale invariance (BSI) and the τCDM 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.