Speeding up N-body simulations of modified gravity: Vainshtein screening models

We introduce and demonstrate the power of a method to speed up current iterative techniques for N-body modified gravity simulations. Our method is based on the observation that the accuracy of the final result is not compromised if the calculation of the fifth force becomes less accurate, but substantially faster, in high-density regions where it is relatively weak due to screening. We focus on the nDGP model which employs Vainshtein screening, and test our method by running AMR simulations in which the fifth force on the finer levels of the mesh (high density) is not obtained iteratively, but instead interpolated from coarser levels. The calculation of the standard gravity component of the force still employs the full AMR structure. We show that the impact this has on the matter power spectrum is below 1% for k < 5h/Mpc at 0z = , and even smaller at higher redshift. The impact on halo properties is also small (≲ 3% for abundance, profiles, mass; and ≲ 0.05% for positions and velocities). The method can boost the performance of modified gravity simulations by more than a factor of 10. This allows them to run on timescales similar to GR simulations and to push them to resolution levels that were previously hard to achieve.