LOCAL NONLINEAR APPROXIMATIONS TO THE GROWTH OF COSMIC STRUCTURES

Local nonlinear approximations to the growth of cosmic perturbations a re developed, resulting in relations at a given epoch, between the pec uliar velocity and gravity fields and their gradients. The continuity equation and the gravitational field are computed exactly at that epoc h, and only the equation of motion is approximated. The second-order r elation is derived for arbitrary geometry and cosmological parameters. Solutions are developed to fourth order for laminar spherical perturb ations in an Einstein-de Sitter universe, with exact mass conservation at all times, but the gain in accuracy for higher orders is modest. A ll orders become important when the specific peculiar kinetic energy b ecomes comparable to the peculiar gravitational potential 1/2v(2) simi lar to phi, typically at relative, density perturbations, delta simila r to 4. The general second-order relation, while implicit, is simple t o solve. N-body simulations show that it provides moderate gains in ac curacy over other local approximations. It can therefore be easily app lied in the comparison of large-scale structures and velocities in the quasi-linear regime, delta similar to 1-4, as well as in the reconstr uction of the primordial perturbations from which they grew.