Constraints on the Power Spectrum of Mass Fluctuations from from Galaxy Cluster Peculiar Velocities

We investigate the feasibility of carrying out likelihood analysis on the velocities of galaxy clusters to determine power spectrum parameters. Using N-body simulations of cosmological density fields we show that the velocity field traced by clusters is highly non-linear on small scales (r < 10 h^-1 Mpc), mostly due to strong infall into superclusters. The transverse and line of sight velocity correlation functions relevant to likelihood analysis deviate significantly from the linear theory values. Unfortunately, the sparseness of cluster samples means that they are not amenable to any rigorous smoothing procedure to rectify this. We are forced instead to remove close pairs of clusters which would contribute disproportionately to the likelihood. This reduces the size still further of the small samples of observed clusters available to us, forcing us into the conclusion that using straightfoward linear theory covariance analysis on clusters is unpromising. Nevertheless we apply the technique to two sets of observational data and find marginal evidence for more power in the mass density field than standard CDM. The normalisation is consistent with \Omega^{0.6}\sigma_{8} \sim 0.7 for both data sets, within the (large) errors.