Strong Coupling and Bounds on the Spin-2 Mass in Massive Gravity

The de Rham-Gabadadze-Tolley theory of a single massive spin-2 field has a cutoff much below its Planck scale because the extra modes from the massive spin-2 multiplet involve higher derivative self-interactions, controlled by a scale convoluted from its mass. Generically, these correct the propagator by environmental effects. The resulting effective cutoff depends on the environmental parameters and the spin-2 “graviton” mass. Requiring the theory to be perturbative down to $\mathcal{O}(1)\mathrm{mm}$, we derive bounds on the mass, corresponding to $\gtrsim \mathcal{O}(1)\mathrm{meV}$ for the generic case, assuming the coupling to be given by the standard Newton’s constant, and somewhat weaker bounds in cases with fine-tuning. Thus, the theory of a single massive spin-2 can really only be viewed as a theory describing the full nonlinear propagation of a massive spin-2 field on a fixed background and not as an approximation to general relativity.