On the Vainshtein mechanism in the minimal model of massive gravity

Abstract: We reinvestigate the fate of the Vainhstein mechanism in the minimal model of dRGT massive gravity. As the latter is characterised by the complete absence of interactions in the decoupling limit, we study their structure at higher energies. We show that in static spherically symmetric configurations, the lowest energy scale of interactions is pushed up to the Planck mass. This fact points towards an absence of Vainshtein mechanism in this framework, but does not prove it. By resorting to the exact vacuum equations of motion, we show that there is indeed an obstruction that precludes any recovery of General Relativity under the conditions of stationarity and spherical symmetry. However, we argue that the latter are too restrictive and might miss some important physical phenomena. Indeed, we point out that in generic non spherically symmetric or time-dependent situations, interactions arising at energies arbitrarily close to the energy scale of the decoupling limit reappear. This leads us to question whether the small degree of spherical symmetry breaking in the solar system can be sufficient to give rise to a successful Vainshtein mechanism.