Exponents of non-linear clustering in scale-free one dimensional cosmological simulations

Abstract

One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent γdepends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κcontrolling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γdepends strongly on both n and κand where it agrees very well with a simple generalisation of the so-called stable clustering hypothesis in three dimensions, and (2) a region in which γis more or less independent of both the spectrum and the expansion of the universe. We explain the observed location of the boundary in (n, κ) space dividing the "stable clustering" region from the "universal" region. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of "universality" of non-linear clustering in this context.

11 pages, 4 figures; new version with minor revisions, published in Monthly Notices (03/2013)

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• Structure formation in a Dirac-Milne universe: comparison with the standard cosmological model
• Cosmology in One Dimension: Vlasov Dynamics
• Stable clustering and the resolution of dissipationless cosmological N-body simulations
• Power spectrum response of large-scale structure in 1D and in 3D: tests of prescriptions for post-collapse dynamics
• Kinetic properties of fractal media
• Dynamics of One-dimensional Self-gravitating Systems Using Hermite-Legendre Polynomials
• Self-similarity and stable clustering in a family of scale-free cosmologies
• Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
• Testing growth rate dependence in cosmological perturbation theory using scale-free models