Clustering of Galaxies with f(R) gravity

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Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by f(R) gravity. We compute the corrected N-particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the f(R) correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of f(R) gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an f(R) gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.