Gravitational partition function modified by superlight braneworld perturbative modes

In this paper, we will analyze the effects of superlight braneworld perturbative modes on clustering of galaxies. In the present manuscript, we use the Boltzmann and Tsallis statistical approaches to study the large distance modification of gravity in the braneworld. The impact of modified potential on clustering of galaxies is analyzed in both the approaches. The infinities associated with Newtonian point mass approximation of gravity models is removed using the analytical extensions. The regularized and finite partition function is obtained for the system of galaxies in the braneworld model and is used to evaluate the regularized thermodynamic properties of the system in the form of equations of state. Hence, we study thermodynamic quantities and discuss about the thermodynamic stability of the model. We find that large number of galaxies may lead to the thermodynamic instability. The appealing feature of the paper revolve around the generalization of the dimensional regularization (GDR) of Bollini and Giambiagi supplemented with the statistical adequacy of Boltzmann and Tsallis.