A key feature of matter density fields in the early universe, predicted by theoretical models, is that density fluctuations must decay in the fastest possible way with scale. In order to understand the subtle properties of these distributions that were overlooked in the literature, we have developed a statistical physics framework to approach the problem of such density fields. In particular we have introduced the concept of super-homogeneous distributions (at the same time Salvatore Torquato and Frenk Stillinger (Princeton) have independently named these systems hyper-uniform) that found ready application in the study of quasi crystals.
We considered the observational implications of super-homogeneity.
In relation with these studies we have considered the generation of initial conditions in cosmological N-body simulations with density correlations prescribed by cosmological theories, a difficult problem because of the discreteness effects inherent to particle distributions. Finally we have also studied the force distribution both in super-homogeneous and inhomogeneous stochastic point processes.