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Summer Research Fellowship Programme of India's Science Academies

STUDY OF LARGE SCALE STRUCTURE FORMATION IN UNIVERSE WITH THE HELP OF BBGKY HIERARCHICAL EQUATIONS

Shankar Ray

Institution: Savitribai Phule Pune University

Dr. Abhirup Datta

Institution: Indian Institute of Technology,Indore

ABSTRACT

The evolution of density correlation in an expanding universe can be explained by BBGKY equations. Here it is studied how the galaxy correlation functions are evolved out of some reasonable initial conditions in the early universe. In case of small amplitude density fluctuation the hierarchy has a natural truncation where one can ignore the reduced three-point correlation function. But in the present universe we cannot go with the linear evolution of the density fluctuation. The density perturbations are evolved enough to be in the non-linear regime due to which there is stong clustering. That is why the two point correlation function ξ(r) is much greater than unity when r<<1 h^(-1) Mpc, and the three point correlation function is of the order of ξ(r)2. In this non-linear situation the hierarchy is dominated by terms that were ignored in linear analyses. The assumption taken to truncate the hierarchy is that the reduced three point correlation function ζ(r) can be expressed as a function of ξ(r). The moments of the BBGKY equations admit a similarity solution if the effect of discreteness of particles can be ignored, the universe approximates the Einstein-de Sitter model and if the matter can be described in the fluid limit.

Keywords: Cosmological Principle, Initial Conditions, Gravitational Instability, Velocity Perturbation

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