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

¹ Departamento de Física Teórica, Universidad Autónoma de Madrid, 28049 Madrid, Spain
² Centro de Investigación Avanzada en Física Fundamental (CIAFF), Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
³ Instituto de Física Teorica UAM-CSIC, c/ Nicolás Cabrera 13–15, Cantoblanco, 28049 Madrid, Spain
⁴ Institut de Física d’Altes Energies (IFAE) The Barcelona Institute of Science and Technology campus UAB, 08193 Bellaterra Barcelona, Spain
⁵ Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
⁶ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
⁷ Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
⁸ Serra Húnter Fellow, Departament de Física, Universitat Autónoma de Barcelona, Edifici C Facultat de Ciències, 08193 Bellaterra, Spain

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 30 June 2025
Accepted: 8 October 2025

Abstract

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.