Cosmological perturbations in Massive Gravity and the Higuchi bound

Abstract

In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound m^2 \geq 2H^2. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity zero mode is a ghost. In contradistinction to previous works, the tension between the Higuchi bound and the Vainshtein mechanism is equally strong regardless of the equation of state for matter.