Js. Bagla et T. Padmanabhan, NONLINEAR EVOLUTION OF DENSITY PERTURBATIONS USING THE APPROXIMATE CONSTANCY OF THE GRAVITATIONAL POTENTIAL, Monthly Notices of the Royal Astronomical Society, 266(1), 1994, pp. 227-237
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.