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.

In this paper, we analyse the effect of the expansion of the universe on the clustering of galaxies. We evaluate the configurational integral for interacting system of galaxies in an expanding universe by including effects produced by the cosmological constant. The gravitational partition function is obtained using this configuration integral. Thermodynamic quantities, specifically, Helmholtz free energy, entropy, internal energy, pressure and chemical potential are also derived for this system. It is observed that they depend on the modified clustering parameter for this system of galaxies. It is also demonstrated that these thermodynamical quantities get corrected because of the cosmological constant.

In this paper, we study thermodynamics of the cluster of galaxies under the effect of dynamical dark energy. We evaluate the configurational integral for interacting system of galaxies in an expanding universe by including the effects produced by the varying Λ. The gravitational partition function is obtained using this configuration integral. We obtain thermodynamics quantities in canonical ensemble which depend on time and investigate the second law of thermodynamics. We also calculate the distribution function in grand canonical ensemble. The time evolution of the clustering parameter of galaxies is investigated for the time dependent (dynamical) dark energy. We conclude that the second law of thermodynamics is valid for the total system of cluster of galaxies and dynamical dark energy. We calculate correlation function and show that our model is very close to Peebles's power law, in agreement with the N-body simulation. It is observed that thermodynamics quantities depend on the modified clustering parameter for this system of galaxies.

In this paper, we analyze the clustering of galaxies using a modified theory of gravity, in which the field content of general relativity has been be increased. This increasing in the field content of general relativity changes the large distance behavior of the theory, and in weak field approximation, it will also modify the large distance behavior of Newtonian potential. So, we will analyzing the clustering of multi-component system of galaxies interacting through this modified Newtonian potential. We will obtain the partition function for this multi-component system, and study the thermodynamics of this system. So, we will analyze the effects of the large distance modification to the Newtonian potential on Helmholtz free energy, internal energy, entropy, pressure and chemical potential of this system. We obtain also the modified distribution function and the modified clustering parameter for this system, and hence observe the effect of large distance modification of Newtonian potential on clustering of galaxies. *

In this paper, we analyze the clustering of galaxies using a modified Newtonian potential. This modification of the Newtonian potential occurs due to the existence of extra dimensions in brane world models. We will analyze a system of galaxies interacting with each other through this modified Newtonian potential. The partition function for this system of galaxies will be calculated, and this partition function will be used to calculate the free energy of this system of galaxies. The entropy and the chemical potential for this system will also be calculated. We will derive explicit expression for the clustering parameter for this system. This parameter will determine the behavior of this system, and we will be able to express various thermodynamic quantities using this clustering parameter. Thus, we will be able to explicitly analyze the effect that modifying the Newtonian potential can have on the clustering of galaxies. We also analyze the effect of extra dimensions on the two-point functions between galaxies.

In this paper, we study the effects of super-light brane world perturbative modes on structure formation in our universe. As these modes modify the large distance behavior of Newtonian potential, they effect the clustering of a system of galaxies. So, we explicitly calculate the clustering of galaxies interacting through such a modified Newtonian potential. We use a suitable approximation for analyzing this system of galaxies, and discuss the validity of such approximations. We observe that such corrections also modify the virial theorem for such a system of galaxies. * Electronic address:

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In a cosmological context, observational best fits for galaxies’ distributions in the Universe have been tackled by recourse to different distribution functions. We provide here arguments favoring the formulation of a rather general distribution function (DF), of Poisson origin, describing galaxy clustering. The DF should be useful irrespective of distances or temperatures. We will be discussing distribution function for gravitational interactions.