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 \hbox { $ { } ^ { \circ } $ } up to a depth of 240 h ^ { -1 } { { Mpc } } .

The power spectrum has been estimated for wave numbers k in the range 0.03 \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } % } k \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 0 % .2 \mbox { $h { { Mpc } } ^ { -1 } $ } .
For k > k _ { { max } } \simeq 0.05 \mbox { $h { { Mpc } } ^ { -1 } $ } the power spectrum of the Abell–ACO clusters has a power–law shape , P ( k ) \propto k ^ { n } , with n \approx - 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 .