Ghosts, strong coupling, and accidental symmetries in massive gravity

We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghostlike degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost, which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbatively, while at larger distances one can use the higher derivative formulation. We also compare massive gravity with other models, namely, deconstructed theories of gravity, as well as the Dvali-Gabadadze-Porrati model. In the latter case, we argue that the Vainshtein recovery process is of a different nature, not involving a ghost degree of freedom.