Nonlinear evolution of density perturbations using approximate constancy of gravitational potential

TL;DR

This paper introduces a new approximation scheme for nonlinear structure formation in the universe, based on the near constancy of gravitational potential during density perturbation evolution, showing improved agreement with simulations.

Contribution

The paper presents a novel approximation method that uses a frozen gravitational potential to model nonlinear evolution, outperforming the Zeldovich approximation and explaining pancake thinness.

Findings

Better agreement with N-body simulations than Zeldovich approximation

Captures shell crossing and particle motion in pancakes

Provides insight into the evolution of the two-point correlation function

Abstract

During the evolution of density inhomogeneties in an $\Omega=1$, matter dominated universe, the typical density contrast changes from $\delta\simeq 10^{-4}$ to $\delta\simeq 10^2$. However, during the same time, 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 nonlinear structures in the universe. This scheme, discussed in this paper, evolves the initial perturbation using a Newtonian gravitational potential frozen in time. We carry out this procedure for different intial spectra and compare the results with the Zeldovich approximation and the frozen flow approximation (proposed by Mattarrese et al. recently). Our results are in far better agreement with the N-body simulations than the Zeldovich approximation. It also provides a dynamical explanation for the fact that pancakes remain thin during the evolution. While there is some superficial similarity between the frozen flow results and ours, they differ considerably in the velocity information. Actual shell crossing does occur in our approximation; also there is motion of particles along the pancakes leading to further clumping. These features are quite different from those in frozen flow model. We also discuss the evolution of the two-point correlation function in various approximations.