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

During the evolution of density inhomogeneities in an OMEGA = 1, matte r-dominated universe, the typical density contrast changes from delta congruent-to 10(-4) to delta congruent-to 10(2). During this time, how ever, the typical value of the gravitational potential generated by th e perturbations changes only by a factor of order unity. This signific ant fact can be exploited to provide a new, powerful approximation sch eme for studying the formation of non-linear structures in the Univers e. The method evolves the initial perturbation using a Newtonian gravi tational potential frozen in time. We carry out this procedure for dif ferent initial spectra and compare the results with the Zeldovich appr oximation and the frozen flow approximation (recently proposed by Mata rrese et al.). Our results are in better agreement with the N-body sim ulations than is the Zeldovich approximation. Our approximation also p rovides 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 flo w model, they differ considerably in the quality of the velocity infor mation produced. Actual shell crossing does occur in our approximation ; there is also motion of particles along the pancakes, leading to fur ther clumping. Some of these features are quite different from those o f the frozen flow model. We also discuss the evolution of the density contrast in various approximations.