Halo Profiles and the Nonlinear Two- and Three-Point Correlation Functions of Cosmological Mass Density

We investigate the nonlinear two- and three-point correlation functions of the cosmological density field in Fourier space and test the popular hierarchical clustering model, that the three-point amplitude Q is independent of scale. In high-resolution N-body simulations of both n=-2 scale-free and cold dark matter models, we find that Q at late times is not constant but increases with wavenumber far into the nonlinear regime. Self-similar scaling also does not hold as rigorously for the three-point function as for the two-point function in the n=-2 simulation, perhaps a manifestation of the finite simulation volume. We suggest that a better understanding of the two- and three-point correlation functions in the nonlinear regime lies in the link to the density profiles of dark matter halos. We demonstrate and quantify how the slopes of the correlation functions are affected by the slope of the halo profiles using simple halo shapes and analytic clustering models.