Massive gravity: a general analysis

Massive gravity can be described by adding to the Einstein-Hilbert action a function V of metric components. By using the Hamiltonian canonical analysis, we find the most general form of V such that five degrees of freedom propagate non perturbatively. The construction is based on a set of differential equations for V, that remarkably can be solved in terms of two arbitrary functions. Besides recovering the known Lorentz invariant massive gravity theory, we find an entirely new class of solutions, with healthy features on the phenomenological side, in particular they are weakly coupled in the solar system and have a high ultraviolet cutoff A(2) = (mM(pl))(1/2), where m is the graviton mass scale.