Massive gravity is not positive

Abstract

We derive new positivity bounds at finite momentum transfer, assuming a large separation between the mass m of the lightest particle in the effective theory and the mass gap M to new heavy states. Massive gravity parametrically violates these bounds unless the cutoff is within 1 order of magnitude of the graviton mass M O(10)m. Nongravitational effective theories of massive spin-2 particles are similarly bounded.