Boltzmann and Tsallis statistical approaches to study quantum corrections at large distances and clustering of galaxies

Abstract

Gravity is so different from other fundamental forces that it is now essentially treated as a nonfundamental force of entropic origin. Several good studies have been carried out in this direction. Quantum gravity is a theory which combines gravity well with quantum physics. However, there are still many impediments to our understanding, especially in the limits of extreme. The effects of quantum gravity start appearing on the scene at Planck length which is the smallest length in nature idealized so far. Although this study incorporates a model which is valid for potential energy corrections at small distances, we have also given a bold try to use it consistently for the corrections at very large distances as well. The model uses two techniques, namely, Boltzmann and Tsallis statistical approaches to explore the thermodynamics within the ambit of the braneworld model giving its further modified version. We have computed the partition function by using both Boltzmann and Tsallis statistical approaches and then used it to study the thermodynamics of the braneworld model. We have analyzed both analytically and graphically, the thermodynamic quantities like Helmholtz free energy and specific heat.