Modified Yang-Lee theory for nonlocal gravitational potential and their phase transition

In this paper, we describe the extension to study the thermodynamics of the structure formation in the large scale Universe in the nonlocal gravity formalism using standard statistical mechanics. From the derivation of the grand partition function in a modified version of the Yang-Lee theory, we obtained the corresponding thermodynamics properties that can be in consistency with a Bose-Einstein dark matter framework and derive its gravitational phase transition.