THE GRAVITY-INDUCED QUASI-GAUSSIAN CORRELATION HIERARCHY

We calculate the correlation hierarchy that first emerges from a Gaussian field, with a given initial spectrum, owing to the nonlinearities of the dynamics in an expanding universe. The mean matter p-point correlation functions are shown to be given by a set of characteristic numbers S(p), so that [delta(p)]c=S(p)[delta-2]p-1 at the lowest order in [delta-2], where [...]c stands for the connected part of the expectation values. These parameters, calculated assuming no cosmological constant, enlarge at every order the results obtained by Peebles and Fry for S3 and S4. They turn out to be completely independent of the initial spectrum, and almost independent of OMEGA. The (Poisson sampling) resulting void probability function, P0, is presented. We find that (1n P0)/nV approximately -(nV-sigma-2)-3/7 for large (nV-sigma-2), where n and sigma-2 are respectively the density and the variance of the field in the volume V. The density distribution is significantly different from a Gaussian distribution and is found to be asymmetrical, always with a positive density, and with an extended large tail for the large overdensities. Extrapolations toward high nonlinear regimes are also discussed.