# Clustering of Galaxies with Dynamical Dark Energy

## TL;DR

This paper explores how dynamical dark energy influences galaxy cluster thermodynamics, including clustering behavior and the validity of the second law, aligning with N-body simulation results.

## Contribution

It introduces a thermodynamic framework for galaxy clusters considering dynamical dark energy, extending previous models to include time-dependent effects and validating the second law.

## Key findings

- Thermodynamics quantities depend on the modified clustering parameter.
- The model aligns with Peebles's power law and N-body simulations.
- The second law of thermodynamics holds for the system.

## Abstract

In this paper, we study thermodynamics of the cluster of galaxies under the effect of dynamical dark energy. We evaluate the configurational integral for interacting system of galaxies in an expanding universe by including the effects produced by the varying $\Lambda$. The gravitational partition function is obtained using this configuration integral. We obtain thermodynamics quantities in canonical ensemble which depend on time and investigate the second law of thermodynamics. We also calculate the distribution function in grand canonical ensemble. The time evolution of the clustering parameter of galaxies is investigated for the time dependent (dynamical) dark energy. We conclude that the second law of thermodynamics is valid for the total system of cluster of galaxies and dynamical dark energy. We calculate correlation function and show that our model is very close to Peebles's power law, in agreement with the N-body simulation. It is observed that thermodynamics quantities depend on the modified clustering parameter for this system of galaxies.