Clustering of Galaxies with f(R) gravity

TL;DR

This paper investigates how f(R) gravity modifies galactic clustering by deriving corrected thermodynamic equations, analyzing stability, and comparing theoretical predictions with observational data.

Contribution

It introduces an analytical correction to the partition function and distribution function for galaxy clustering under f(R) gravity, providing new insights into cosmic structure formation.

Findings

f(R) gravity affects the power-law behavior of correlation functions

Derived equations of state incorporate f(R) corrections

Results are consistent with observational galaxy cluster data

Abstract

Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by $f(R)$ gravity. We compute the corrected $N$-particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the $f(R)$ correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of $f(R)$ gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an $f(R)$ gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.