Gravitational dynamics of an infinite shuffled lattice: early time evolution and universality of non-linear correlations

TL;DR

This paper investigates the early non-linear evolution of gravitational clustering in an infinite shuffled lattice, revealing a two-phase process and explaining the universality of non-linear correlations across different initial conditions.

Contribution

It introduces a two-phase approximation for early gravitational clustering and explains the universality of non-linear correlations in shuffled lattice and Poisson initial conditions.

Findings

Early non-linear correlations can be modeled by a two-phase process.

The initial perturbative phase transforms the lattice into a Poisson distribution.

Universality of non-linear clustering is explained by the two-phase evolution.

Abstract

In two recent articles a detailed study has been presented of the out of equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this article we extend the treatment of the early time phase during which strong non-linear correlations first develop, prior to the onset of ``self-similar'' scaling in the two point correlation function. We establish more directly, using appropriate modifications of the numerical integration, that the development of these correlations can be well described by an approximation of the evolution in two phases: a first perturbative phase in which particles' displacements are small compared to the lattice spacing, and a subsequent phase in which particles interact only with their nearest neighbor. For the range of initial amplitudes considered we show that the first phase can be well approximated as a transformation of the perturbed lattice configuration into a Poisson distribution at the relevant scales. This appears to explain the ``universality'' of the spatial dependence of the asymptotic non-linear clustering observed from both shuffled lattice and Poisson initial conditions.