Abstract
In this manuscript, we have explored the large-scale structure (LSS) of the Universe using the halo approximation of galaxies and the mean-field (mean-field approximation) theory of galaxy clusters. Employing the modified gravitational potential, which relies on Boltzmann’s statistics, we have analyzed the effect of galaxy clusters on the large-scale structure of the Universe. With both of these approximations, we have observed the significance of the modified potential. Also, the gravitational partition function obtained from the applied approximations has been used to determine the thermodynamic properties of these galaxy clusters. Besides this, the impact of these approximations on the derived quantities, such as Helmholtz free energy, entropy, internal energy, pressure, and chemical potential, was observed and is also evident from their respective plots along with their distribution functions. Importantly, the divergence of configurational integrals has been removed through the said approach.
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