Transients from initial conditions based on Lagrangian perturbation theory inN-body simulations

Abstract

We explore the initial conditions for cosmologicalN-body simulations suitable for calculating the skewness and kurtosis of thedensity field. In general, the initial conditions based on the perturbation theoryprovide incorrect second-order and higher-order growth. These errors impliedby the use of the perturbation theory to set up the initial conditions inN-body simulations are called transients. Unless these transients are completely suppressed comparedwith the dominant growing mode, we cannot reproduce the correct evolution of cumulants withorders higher than two, even though there is no problem with the numerical scheme. Weinvestigate the impact of transients on the observable statistical quantities by performingN-body simulations with initial conditions based on Lagrangian perturbation theory. Weshow that the effects of transients on the kurtosis from the initial conditions, based onsecond-order Lagrangian perturbation theory (2LPT), have almost disappeared byz∼5, as long as the initialconditions are set at z>30. This means that for practical purposes, the initial conditions based on 2LPT are accurateenough for numerical calculations of skewness and kurtosis.