We test an analytic model for the two-point correlations of galaxy clusters in redshift space using the Hubble Volume N-body simulations .
The correlation function of clusters shows no enhancement along the line of sight , due to the lack of any virialised structures in the cluster distribution .
However , the distortion of the clustering pattern due to coherent bulk motions is clearly visible .
The distribution of cluster peculiar motions is well described by a Gaussian , except in the extreme high velocity tails .
The simulations produce a small but significant number of clusters with large peculiar motions .
The form of the redshift space power spectrum is strongly influenced by errors in measured cluster redshifts in extant surveys .
When these errors are taken into account , the model reproduces the power spectrum recovered from the simulation to an accuracy of 15 \% or better over a decade in wavenumber .
We compare our analytic predictions with the power spectrum measured from the APM cluster redshift survey .
The cluster power spectrum constrains the amplitude of density fluctuations , as measured by the linear rms variance in spheres of radius 8 h ^ { -1 } Mpc , denoted by \sigma _ { 8 } .
When combined with the constraints on \sigma _ { 8 } and the density parameter \Omega derived from the local abundance of clusters , we find a best fitting cold dark matter model with \sigma _ { 8 } \approx 1.25 and \Omega \approx 0.2 , for a power spectrum shape that matches that measured for galaxies .
However , for the best fitting value of \Omega and given the value of Hubble ’ s constant from recent measurements , the assumed shape of the power spectrum is incompatible with the most readily motivated predictions from the cold dark matter paradigm .