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

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.

11 pages, 11 figures, shortened introductory sections and other minor modifications, version to appear in Phys. Rev. E

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Cited by in corpus (8)

• Discreteness Effects in Lambda Cold Dark Matter Simulations: A Wavelet-Statistical View
• Towards quantitative control on discreteness error in the non-linear regime of cosmological N body simulations
• 1-d gravity in infinite point distributions
• Non-linear gravitational clustering of cold matter in an expanding universe: indications from 1D toy models
• Exponents of non-linear clustering in scale-free one dimensional cosmological simulations
• Dynamics of finite and infinite self-gravitating systems with cold quasi-uniform initial conditions
• Self-similarity and stable clustering in a family of scale-free cosmologies
• Testing growth rate dependence in cosmological perturbation theory using scale-free models