Force equation of the large-scale structure of the Universe

This article presents a statistical-mechanical treatment of a relationship (the force equation) between the gravitational potential for two particles and the correlation functions in a relaxed distribution of particles with different masses. This relationship is used in the case of galaxies interacting through a Newtonian potential in an Universe in expansion, i.e. the large-scale distribution of galaxies. By applying this equation and from the observed two-point correlation function for galaxies as a $-1.8$ exponent power law, I derive the approximate dependence of a mass-mass correlation function as a $-2.8$ exponent power law, i.e. I infer that mass is more correlated than galaxies at short distances, when the distribution is considered as relaxed.