  We discuss the galaxy clustering based on thermodynamics and statistical
mechanics in the expanding universe in a modified theory of gravity. The
modified general relativity (MGR) is developed using the regular line element
field to construct a symmetric tensor that represents the energy momentum of
the gravitational field. This in turn provides a modified gravitational
potential with terms that represent dark matter and dark energy effects without
actually invoking the two. Based on the modified gravitational potential we
calculate the distribution function of the galaxies. We also calculate various
thermodynamic equations of state. We make a data analysis of the data obtained
through the SDSS-III survey and check the feasibility of the theoretical model
of probability distribution of galaxies in the universe.
