Higher Order Moments of the Matter Distribution in Scale--Free Cosmological Simulations with Large Dynamic Range

Abstract

We calculate reduced moments ${\overline{\xi }}_q$ of the matter density fluctuations, up to order $q=5$, from counts in cells produced by Particle--Mesh numerical simulations with scale--free Gaussian initial conditions. We use power--law spectra $P(k)\propto k^n$ with indices $n=-3,-2,-1,0,1$. Due to the supposed absence of characteristic times or scales in our models, all quantities are expected to depend on a single scaling variable. For each model, the moments at all times can be expressed in terms of the variance ${\overline{\xi }}_2$, alone. We look for agreement with the hierarchical scaling ansatz, according to which ${\overline{\xi }}_q\propto {\overline{\xi }}_2^{q-1}$. For $n\le -2$ models we find strong deviations from the hierarchy, which are mostly due to the presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also found in $n\ge -1$ models. For the first time, due to our large dynamic range and careful checks of scaling and shot--noise effects, we are able to detect evolution away from the perturbation theory result.

24 pages in Tex, DAPD 220

Cited by in corpus (11)

• Non-Linear Evolution of the Bispectrum of Cosmological Perturbations
• Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
• Cosmological Perturbations: Entering the Non-Linear Regime
• Scaling in the Universe
• Cosmic Statistics of Statistics
• Effects of Sampling on Statistics of Large Scale Structure
• The mass density field in simulated non-Gaussian scenarios
• From Snakes to Stars, the Statistics of Collapsed Objects - II. Testing a Generic Scaling Ansatz for Hierarchical Clustering
• Higher order moments of the density field in a parameterized sequence of non-gaussian theories
• Constraining Primordial Non-Gaussianity with Moments of the Large Scale Density Field
• Statistics of Cosmological Inhomogeneities