On the Reliability of Initial Conditions for Dissipationless Cosmological Simulations

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Abstract
We present the study of ten random realisations of a density field characterised by a cosmological power spectrum P(k) at redshift z = 50. The reliability of such initial conditions for N-body simulations is tested with respect to their correlation properties. The power spectrum P(k) and the mass variance σM(r) do not show detectable deviations from the desired behaviour in the intermediate range of scales between the mean interparticle distance and the simulation volume. The estimator for ξ(r) is too noisy to detect any reliable signal at the initial redshift z = 50. The particle distributions are then evolved forward until z = 0. This allows us to explore the cosmic variance stemming from the random nature of the initial conditions. With cosmic variance we mean the fact that a simulation represents a single realisation of the stochastic initial conditions whereas the real Universe contains many realisations of regions of the size of the box; this problem affects most importantly the scales at about the fundamental mode. We study morphological descriptors of the matter distribution such as the genus, as well as the internal properties of the largest object(s) forming in the box. We find that the scatter is at least comparable to the scatter in the fundamental mode.

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