# Thermodynamics and galactic clustering with a modified gravitational potential

## TL;DR

This paper investigates how quantum, logarithmic, and cosmological constant corrections to gravity influence galactic clustering and large-scale structure formation using thermodynamics and analytical $N$-body partition functions.

## Contribution

It introduces a novel thermodynamic framework incorporating quantum and cosmological corrections to analyze galactic clustering and derives modified correlation functions.

## Key findings

- Derived exact equations of state with corrections
- Identified a modified clustering parameter
- Found deviations in two-point correlation functions

## Abstract

Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the cosmological constant ($\Lambda$) in the formation of the large scale structure of the Universe. We derive the $N$-body partition function for extended-mass galaxies (galaxies with halos) analytically. For this partition function, we compute the exact equations of states, which exhibit the logarithmic, volume and cosmological constant corrections. In this setting, a modified correlation (clustering) parameter (due to these corrections) emerges naturally from the exact equations of state. We compute a corrected grand canonical distribution function for this system. Furthermore, we obtain a deviation in differential forms of the two-point correlation functions for both the point-mass and extended-mass cases. The consequences of these deviations on the correlation function's power law are also discussed.