The gravity-induced quasi-Gaussian correlation hierarchy

The hierarchy that first emerges from a Gaussian field, with a given initial spectrum, owing to the nonlinearities of the dynamics in an expanding universe, is calculated. 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.