Non-linear dynamics of the minimal theory of massive gravity

Abstract: We investigate cosmological signatures of the minimal theory of massive gravity (MTMG). To this aim, we simulate the normal branch of the MTMG by employing the \textsc{Ramses} \mbox{$N$-body} code and extending it with an effective gravitational constant $G_{\rm eff}$. We implement an environment-dependent $G_{\rm eff}$ as a function of the graviton mass and the local energy density as predicted by MTMG. We find that halo density profiles are not a good probe for MTMG, because deviations from general relativity (GR) are quite small. Similarly, the matter power spectra show deviations only at the percentage level. However, we find a clear difference between MTMG and GR in that voids are denser in MTMG than in GR. As measuring void profiles is quite a complex task from an observational point of view, a better probe of MTMG would be the halo abundances. In this case, MTMG creates a larger amount of massive halos, while there is a suppression in the abundance of small halos.