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In this paper, we will analyze the effects of super-light brane worldperturbative modes on clustering of galaxies. In present manuscript, we use theBoltzmann and Tsallis statistical approaches to study the large distancemodification of gravity in the brane world. The impact of modified potential onclustering of galaxies is analyzed in both the approaches. The infinitiesassociated with Newtonian point mass approximation of gravity models is removedusing the analytical extensions. The regularized and finite partition functionis obtained for the system of galaxies in the brane world model and is used toevaluate the regularized thermodynamic properties of the system in the form ofequations of state. Hence, we study thermodynamic quantities and discuss aboutthe thermodynamic stability of the model. We find that large number of galaxiesmay lead to the thermodynamic instability.

Gravitational partition function modified by super-light brane world perturbative modes