PERTURBATIVE GROWTH OF COSMOLOGICAL CLUSTERING .2. THE 2-POINT CORRELATION

We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two-point correlation and th e pair velocity for Gaussian initial conditions in a critical density matter-dominated cosmological model. We compare our results with the r esults obtained using the hydrodynamic equations that neglect pressure and find that the two match, indicating that there are no effects of multistreaming at this order of perturbation. We analytically study th e effect of small scales on the large scales by calculating the nonlin ear correction for a Dirac delta function initial two-point correlatio n. We find that the induced two-point correlation has a x(-6) behavior at large separations. We have considered a class of initial condition s where the initial power spectrum at small k has the form k(n) with 0 < n less than or equal to 3 and have numerically calculated the nonli near correction to the two-point correlation, its average over a spher e and the pair velocity over a large dynamical range. We find that at small separations the effect of the nonlinear term is to enhance the c lustering, whereas at intermediate scales it can act to either increas e or decrease the clustering. At large scales we find a simple formula that gives a very good fit for the nonlinear correction in terms of t he initial function. This formula explicitly exhibits the influence of small scales on large scales and because of this coupling the perturb ative treatment breaks down at large scales much before one would expe ct it to if the nonlinearity were local in real space. We physically i nterpret this formula in terms of a simple diffusion process. We have also investigated the case n = 0, and we find that it differs from the other cases in certain respects. We investigate a recently proposed s caling property of gravitational clustering, and we find that the lowe st order nonlinear terms cause deviations from the scaling relations t hat are strictly valid in the linear regime. The approximate validity of these relations in the nonlinear regime in l(T)-body simulations ca nnot be understood at this order of evolution.