A simple method for computing the nonlinear mass correlation function with implications for stable clustering

We propose a simple and accurate method for computing analytically the mass correlation function for cold dark matter and scale-free models that fits N-body simulations over a range that extends from the linear to the strongly nonlinear regime. The method, based on the dynamical evolution of the pair-conservation equation, relies on a universal relation between the pairwise velocity and the smoothed correlation function valid for high- and low-density models, as derived empirically from N-body simulations. An intriguing alternative relation, based on the stable-clustering hypothesis, predicts a power-law behavior of the mass correlation function that disagrees with N-body simulations but conforms well to the observed galaxy correlation function if negligible bias is assumed. The method is a useful tool for rapidly exploring a wide span of models and, at the same time, raises new questions about large-scale structure formation.