Accurate N -body simulations with local primordial non-Gaussianities: Initial conditions and aliasing

The new generation of galaxy surveys designed to constrain local primordial non-Gaussianity (PNG) requires N-body simulations that accurately reproduce its effects. In this work, we explore various prescriptions for the initial conditions of simulations with PNG, seeking to optimise accuracy and minimise numerical errors, particularly due to aliasing. We used 186 runs that vary the starting redshift, Lagrangian Perturbation Theory (LPT) order, and non-Gaussianities (f _NL^local and g _NL^local). Starting with third order LPT (3LPT) at a redshift as low as z _start ≃ 11.5 reproduces to <1% the power spectrum, bispectrum, and halo mass function of a high-resolution reference simulation. The aliasing induced by the PNG terms in the power spectrum produces a ≤3% excess for small-scales at the initial conditions. This excess drops below 0.1% by z = 0. State-of-the-art initial condition generators show a sub-percent agreement. We show that initial conditions for simulations with PNG should be established at a lower redshift using higher-order LPT schemes. We also show that removing the PNG aliasing signal is unnecessary for current simulations. The methodology proposed here can accelerate the generation of simulations with PNG while enhancing their accuracy.