Evolution of velocity and density fields around clusters of galaxies

The evolution of the averaged density and infall velocity profiles around clusters of galaxies is explored in several cosmological scenarios based on gravitational instability. The analysis is based on the statistics peaks in random Gaussian fields and the spherical infall model. This method is shown to give accurate predictions of the cluster-galaxy cross-correlation function when compared with N-body simulations. The predictions for the average infall velocity as function of radius are not as accurate but are still useful. The discrepancy is probably caused by shear in the velocity field. The predictions for the cluster-galaxy cross-correlation function on large scales are very different for models with little power on large scales (such as the cold dark matter and the hot dark matter models) and models with much power on large scales (such as primordial isocurvature baryon models). The ensemble average infall velocity as a function of radius, if it is possible to measure it, provides a useful method for distinguishing between models with different levels of biasing of the galaxy number density fluctuations relative to mass fluctuations. Observations of the density and velocity profiles in one supercluster (i. e. , the Local Supercluster) are of limited value for setting constraints on models of structure formation in the universe. However, the r^-1^ dependence of the velocity field in the Local Supercluster is in good agreement with the predictions of the cold dark matter model, contrary to some claims.