Resolving the Ghost Problem in Nonlinear Massive Gravity

We analyze the ghost issue in the recently proposed models of nonlinear massive gravity in the Arnowitt-Deser-Misner formalism. We show that, in the entire two-parameter family of actions, the Hamiltonian constraint is maintained at the complete nonlinear level and we argue for the existence of a nontrivial secondary constraint. This implies the absence of the pathological Boulware-Deser ghost to all orders. To our knowledge, this is the first demonstration of the existence of a consistent theory of massive gravity at the complete nonlinear level, in four dimensions.