PySCo-EFT and ECOSMOG-EFT: a tandem of N-body simulation codes for the effective field theory of dark energy

Modified gravity theories constitute viable alternatives to the standard cosmological model for explaining the observed late-time accelerated expansion of the Universe. The effective field theory of dark energy (EFTofDE) is an efficient framework to describe a wide range of such theories with a limited number of parameters. To robustly constrain these theories, high-resolution cosmological N-body simulations are required to obtain accurate predictions for the matter distribution on non-linear scales, which can then be quantitatively compared with clustering and weak gravitational lensing measurements from forthcoming galaxy surveys. We introduce two new N-body simulation codes for cosmologies governed by cubic luminal Horndeski gravity models of the EFTofDE under quasi-static approximation: , a fast Python-based particle-mesh code, and , an accurate -based code with adaptive mesh refinement. We used iterative solvers and multigrid schemes to solve for the additional scalar field equation in both codes, including the non-linear Vainshtein screening mechanism. The standard gravitational force was augmented by a fifth force from the scalar field. We present several validation and convergence tests of the codes. We obtained a sub 0.5% agreement with linear theory on large scales and a similar agreement between the two codes in particle-mesh mode for the power spectrum boost, although they implement different solvers. The dominant numerical effects on the matter power spectrum boost are finite mass resolution, finite-volume effects, refinement threshold, and starting redshift, but they are limited to below 2% at the largest wavenumbers, k=10,h , ^ PySCo-EFT ECOSMOG-EFT RAMSES Mpc -1 , for the range of tested values. Finally, we investigated the impact of the EFTofDE parameters on the matter power spectrum ratios between EFTofDE and Lambda cold dark matter scenarios. Depending on the values of the EFTofDE parameters, the screening can play a negligible or dominant role compared to the often-used linearised field equations. Our codes provide tools for generating fast and accurate predictions of the impact of the EFTofDE on the clustering of matter, incorporating the non-linear Vainshtein screening mechanism.