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

TL;DR

This paper explores quantum gravity effects at large distances using Boltzmann and Tsallis statistics within a brane world model, analyzing thermodynamic stability and properties of galaxy clustering.

Contribution

It introduces a novel application of Boltzmann and Tsallis statistical methods to study quantum corrections at large scales in a brane world context.

Findings

Partition functions computed for both statistical approaches.

Analysis of Helmholtz free energy and specific heat.

Discussion on thermodynamic stability related to galaxy number.

Abstract

Gravity is so different from other fundamental forces that it is now essentially treated as a non-fundamental force of entropic origin. A number of good studies have been carried out in this direction. Quantum gravity has also significantly improved our understanding by combining 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. While as this study incorporates a model which is valid for potential energy corrections at small distances but we have also given a bold try to use it confidently 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 brane world model giving its further modified version. We have computed partition function by using both Boltzmann and Tsallis statistical approaches and then used it to study thermodynamics of the brane world model. We have analyzed both analytically and graphically, the thermodynamic quantities like Helmholtz free energy and specific heat. The thermodynamic stability of the model is also discussed depending on the number of galaxies.