Perturbative growth of cosmological clustering. I: Formalism

Abstract

Here we rederive the hierarchy of equations for the evolution of distribution functions of various orders using a convenient parameterization. We use this to obtain equations for evolving the two-and three-point correlation functions in powers of a small parameter, viz., the initial density contrast. The correspondence of the lowest order solutions of these equations to the results from the linear theory of density perturbations is shown for an Omega=1 universe. These equations are then used to calculate, to the lowest order, the induced three-point correlation function that arises from Gaussian initial conditions in an Omega=1 universe. We obtain an expression which explicitly exhibits the spatial structure of the induced three-point correlation function. It is seen that the spatial structure of this quantity is independent of the value of Omega. We also calculate the triplet momentum. We find that the induced three-point correlation function does not have the 'hierarchical' form often assumed. We discuss possibilites of using the induced three-point correlation to interpret observational data. The formalism developed here can also be used to test a validity of different schemes to close the BBGKY hierarchy.