Euclid preparation LXII. Simulations and non-linearities beyond Lambda cold dark matter. 1. Numerical methods and validation

Abstract

To constrain cosmological models beyond Lambda CDM, the development of the Euclid analysis pipeline requires simulations that capture the non-linear phenomenology of such models. We present an overview of numerical methods and N-body simulation codes developed to study the non-linear regime of structure formation in alternative dark energy and modified gravity theories. We review a variety of numerical techniques and approximations employed in cosmological N-body simulations to model the complex phenomenology of scenarios beyond Lambda CDM. This includes discussions on solving non-linear field equations, accounting for fifth forces, and implementing screening mechanisms. Furthermore, we conduct a code comparison exercise to assess the reliability and convergence of different simulation codes across a range of models. Our analysis demonstrates a high degree of agreement among the outputs of different simulation codes, typically within 2% for the predicted modification of the matter power spectrum and within 4% for the predicted modification of the halo mass function, although some approximations degrade accuracy a bit further. This provides confidence in current numerical methods of modelling cosmic structure formation beyond Lambda CDM. We highlight recent advances made in simulating the non-linear scales of structure formation, which are essential for leveraging the full scientific potential of the forthcoming observational data from the Euclid mission.