Accurate initial conditions for cosmological N-body simulations: minimizing truncation and discreteness errors

Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the theory side, initial conditions are usually provided by using low-order truncations of the displacement field from Lagrangian perturbation theory, with the first- and second-order approximations being the most common ones. Here, we investigate the improvement brought by using initial conditions based on third-order Lagrangian perturbation theory (3LPT). We show that with 3LPT, truncation errors are vastly suppressed, thereby opening the portal to initializing simulations accurately as late as z = 12 (for the resolution we consider). We analyse the competing effects of perturbative truncation and particle discreteness on various summary statistics. Discreteness errors are essentially decaying modes and thus get strongly amplified for earlier initialization times. We show that late starting times with 3LPT provide the most accurate configuration, which we find to coincide with the continuum fluid limit within 1 per cent for the power- and bispectrum at z = 0 up to the particle Nyquist wavenumber of our simulations (k similar to 3h Mpc(-1)). In conclusion, to suppress non-fluid artefacts, we recommend initializing simulations as late as possible with 3LPT. We make our 3LPT initial condition generator publicly available.