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

We explore the initial conditions for cosmological N-body simulations suitable for calculating the skewness and kurtosis of the density field. In general, the initial conditions based on the perturbation theory (PT) provide incorrect second-order and higher-order growth. These errors implied by the use of the perturbation theory to set up the initial conditions in N-body simulations are called transients. Unless these transients are completely suppressed compared with the dominant growing mode, we can not reproduce the correct evolution of cumulants with orders higher than two, even though there is no problem with the numerical scheme. We investigate the impact of transients on the observable statistical quantities by performing $N$-body simulations with initial conditions based on Lagrangian perturbation theory (LPT). We show that the effects of transients on the kurtosis from the initial conditions, based on second-order Lagrangian perturbation theory (2LPT) have almost disappeared by $z\sim5$, as long as the initial conditions are set at $z > 30$. This means that for practical purposes, the initial conditions based on 2LPT are accurate enough for numerical calculations of skewness and kurtosis.