Resummation of massive gravity

We construct four-dimensional covariant nonlinear theories of massive gravity which are ghost-free in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an effective field theory of massive gravity. We show that away from the decoupling limit the Hamiltonian constraint is maintained at least up to and including quartic order in nonlinearities, hence excluding the possibility of the Boulware-Deser ghost up to this order. We also show that the same remains true to all orders in a similar toy model.