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

Abstract

One-dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three-dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three-dimensional Einstein-de Sitter (EdS) model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by powerlaw behaviour of the two-point correlation function.We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalization of the so-called stable clustering hypothesis in three dimensions; and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the 'stable clustering' region from the 'universal' region is very well approximated by a 'critical' value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis.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. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.