The problem of cosmological dark matter and statistical physics

Although dark matter is supposed to provide with more than 0.9 of the total fraction of the mass-energy in universe, its amount and properties can only be defined a posteriori. In this context, a crucial point concerns the identification of a possible clear feature of dark matter fields which is not arbitrary, i.e. a property which has to be satisfied by dark matter fluctuations under some very general theoretical conditions. We discuss the fact that this property, in standard cosmological models, is represented by super-homogeneity, i.e. a very fine tuned balance between negative and positive correlations of density fluctuations, which must be imprinted both in the anisotropies of the CMBR and in the large scale distribution of galaxies. We review the main aspects of this property, considering examples of super-homogeneous systems well-studied in statistical physics, and discuss its possible observational evidences.