Gravitational clustering of galaxies in an expanding universe

We inquire the phenomena of clustering of galaxies in an expanding universe from a theoretical point of view on the basis of thermodynamics and correlation functions. The partial differential equation is developed both for the point mass and extended mass structures of a two-point correlation function by using thermodynamic equations in combination with the equation of state taking gravitational interaction between particles into consideration. The unique solution physically satisfies a set of boundary conditions for correlated systems and provides a new insight into the gravitational clustering problem.