Cosmological perturbations in massive gravity and the Higuchi bound

Abstract

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