T. Padmanabhan — Page 13

arXiv1993

Nonlinear evolution of density perturbations using approximate constancy of gravitational potential

During the evolution of density inhomogeneties in an $Ω=1$, matter dominated universe, the typical density contrast changes from $δ\simeq 10^{-4}$ to $δ\simeq 10^2$. 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.

gr-qc↗

arXiv1993

Scaling properties of the gravitational clustering in the nonlinear regime

The growth of density perturbations in an expanding universe in the non-linear regime is investigated. The underlying equations of motion are cast in a suggestive form, and motivate a conjecture that the scaled pair velocity, $h(a,x)\equiv -[v/(\dot{a}x)]$ depends on the expansion factor $a$ and comoving coordinate $x$ only through the density contrast $σ(a,x)$. This leads to the result that the true, non-linear, density contrast $<(δρ/ρ)^{2}_{x}>^{1/2}=σ(a,x)$ is a universal function of the density contrast $σ_L(a,l)$, computed in the linear theory and evaluated at a scale $l$ where $l=x(1+σ^2)^{1/3}$. This universality is supported by existing numerical simulations with scale-invariant initial conditions having different power laws. We discuss a physically motivated ansatz $h(a,x)=h[σ^2(a,x)]$ and use it to compute the non-linear density contrast at any given scale analytically. This provides a promising method for analysing the non-linear evolution of density perturbations in the universe and for interpreting numerical simulations.

gr-qc↗