On the integration of the BBGKY equations for the development of strongly nonlinear clustering in an expanding universe

The BBGKY equations describing the evolution of the galaxy correlation functions in an expanding universe are integrated numerically in order to discover those conditions (if any) under which the predicted functions would match the observations. The BBGKY equations for the n-point correlation functions in position and velocity are adopted from the theory of nonideal gases, and the empirical finding that the three-point spatial correlation function can be accurately represented as a simple function of the two-point correlation function is employed along with a consistency constraint to obtain a possible form for the three-point spatial and velocity function in terms of the two-point function. The BBGKY hierarchy is closed in this manner, and the resulting nonlinear integrodifferential equation is simplified to the point where numerical solution is practical. Numerical results are presented and evaluated for various values of the spectral index of the initial density perturbation.