Cosmic energy equation for extended structures and its application to gravitational galaxy clustering

Cosmic energy equation represents the law of conservation of energy in the region expanding with time as the universe expands. It gives the evolution of kinetic and correlation potential energy with time in a cluster expanding as the universe expands. To understand the clustering of galaxies under the influence of gravitational force, cosmic energy equation is of great help. We use cosmic energy equation for extended structures (galaxies with halos) to analyse the gravitational galaxy clustering in different ways. We try to understand the influence of expansion on the clustering by deriving the relation between correlation parameter b _V and scale factor R. We also derive the relation between the peculiar kinetic energy K and correlation parameter to know that when peculiar kinetic energy dominates over the kinetic energy of galaxies due to expansion. Besides, the evolution of specific heat and energy provides the information regarding the different states of clustering.