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 one order of magnitude of the graviton mass $M\lesssim O(10)m$. Non-gravitational effective theories of massive spin-2 particles are similarly bounded.

Comments: v2: 8 pages + appendices & references, 3 figures. Typos fixed, references added, discussion on negativity of general spin-2 EFTs included