Matter Power Spectra in Modified Gravity: A Comparative Study of Approximations and 𝑁-Body Simulations

Testing gravity and the concordance model of cosmology, ΛCDM, at large scales is a key goal of this decade’s largest galaxy surveys. Here we present a comparative study of dark matter power spectrum predictions from different numerical codes in the context of three popular theories of gravity that induce scale-independent modifications to the linear growth of structure: nDGP, Cubic Galileon and K-mouflage. In particular, we compare the predictions from 𝑁-body simulations solving the full scalar field equation, two 𝑁-body codes with approximate time integration schemes, a parametrised modified 𝑁-body implementation and
the analytic halo model reaction approach. We find the modification to the ΛCDM spectrum is in 2% agreement at 𝑧 ≤ 1 and 𝑘 ≤ 1 ℎ/Mpc over all gravitational models and codes, in accordance with many previous studies, indicating these modelling approaches are robust enough to be used in forthcoming survey analyses under appropriate scale cuts. We further make public the new code implementations presented, specifically the halo model reaction K-mouflage implementation and the relativistic Cubic Galileon implementation.