The spherical infall model in a cosmological background density field

We discuss the influence of the cosmological background density field on th e spherical infall model. The spherical infall model has been used in the P ress-Schechter formalism to evaluate the number abundance of clusters of ga laxies, as well as to determine the density parameter of the Universe from the infalling flow. Therefore, the understanding of collapse dynamics plays a key role for extracting cosmological information. Here, we consider a mo dified version of the spherical infall model. We derive the mean field equa tions from the Newtonian fluid equations, in which the influence of cosmolo gical background inhomogeneity is incorporated into the averaged quantities as the backreaction. By calculating the averaged quantities explicitly, we obtain simple expressions and find that, in the case of a scale-free power spectrum, density fluctuations with a negative spectral index make the inf alling velocities slow. This suggests that we underestimate the density par ameter Omega when using the simple spherical infall model. In cases with th e index n > 0, the effect of background inhomogeneity could be negligible a nd the spherical infall model becomes a good approximation for infalling fl ows. We also present a realistic example with a cold dark matter power spec trum. In this case, the mean infall tends to be slow owing to the anisotrop ic random velocity.