NONLINEAR EVOLUTION OF DENSITY PERTURBATIONS USING THE APPROXIMATE CONSTANCY OF THE GRAVITATIONAL POTENTIAL

During the evolution of density inhomogeneities in an OMEGA = 1, matter-dominated universe, the typical density contrast changes from delta congruent-to 10(-4) to delta congruent-to 10(2). During this time, however, the typical value of the gravitational potential generated by the perturbations changes only by a factor of order unity. This significant fact can be exploited to provide a new, powerful approximation scheme for studying the formation of non-linear structures in the Universe. The method evolves the initial perturbation using a Newtonian gravitational potential frozen in time. We carry out this procedure for different initial spectra and compare the results with the Zeldovich approximation and the frozen flow approximation (recently proposed by Matarrese et al.). Our results are in better agreement with the N-body simulations than is the Zeldovich approximation. Our approximation also provides a dynamical explanation for the fact that pancakes remain thin during the evolution of density inhomogeneities. While there is some superficial similarity between our results and those of the frozen flow model, they differ considerably in the quality of the velocity information produced. Actual shell crossing does occur in our approximation; there is also motion of particles along the pancakes, leading to further clumping. Some of these features are quite different from those of the frozen flow model. We also discuss the evolution of the density contrast in various approximations.