Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes

We consider the long-standing problem of predicting the hierarchical clustering amplitudes Sp in the strongly non-linear regime of gravitational evolution. N-body results for the nonlinear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, S3, starting from leading-order perturbation theory. When generalized to higherorder (p > 3) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the nonlinear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum. Subject headings: cosmology: theory, cosmology: large-scale structure of universe; methods: numerical; methods: analytical