The most prominent feature of the Iinitial conditions of the matter density field in the early universe, in standard theoretical models, derived from inflationary mechanisms, is that matter density field presents on large scale super-homogeneous features. This means the following. If one considers the paradigm of uniform distributions, the Poisson process where particles are placed completely randomly in space, the mass fluctuations in a sphere of radius R growths as the volume of the sphere. A super-homogeneous distribution is a system where the average density is well defined (i.e., it is uniform) and where fluctuations in a sphere grow slowe than in the Poisson case, like the surface of the spherical volume of radius R :in this case there are the so-called surface fluctuations to differentiate them from Poisson-like volume fluctuations.

A well known system in statistical physics systems of this kind is the one component plasma [OCP) which is characterized by a dynamics which at thermal equilibrium gives rise to such configurations. The OCP is simply a system of charged point particles interacting through a repulsive 1/r potential, in a uniform background which gives overall charge neutrality. Simple modifications of the OCP can produce equilibrium correlations of the kind assumed in the cosmological context .

For the particular form of primordial cosmological spectra, theoretical density fields in the early universe are characterized by a negative power-law behavior in the reduced correlation function at large separations. The clarification of these properties, which correspond to a global fine-tuning of positive and negative correlations, allow us to define the strategy to measure such signals in real galaxy samples and to identify several problems concerning, for example, the effects related to sampling (galaxy distribution can be regarded as a sampling of the underlying dark matter density field).

Another reason for the interested in the study of super-homogeenlous density fields concerns the problems of the generation of point distributions with this kind of correlation properties. These are point configurations which can be used as initial conditions in gravitational N-body simulations , both to genarate point distributions with correlation properrties as those predicted by standard cosmological moldes, and to study questions related to the gravitational evolution of this kind of systems