Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity

A bstract In massive gravity and in bimetric theories of gravity, two constraints are needed to eliminate the two phase-space degrees of freedom of the Boulware-Deser ghost. For recently proposed non-linear theories, a Hamiltonian constraint has been shown to exist and an associated secondary constraint was argued to arise as well. In this paper we explicitly demonstrate the existence of the secondary constraint. Thus the Boulware-Deser ghost is completely absent from these non-linear massive gravity theories and from the corresponding bimetric theories. Equivalently, this proves the existence of classically ghost-free theories of massive spin-2 fields, in both fixed and dynamical gravitational backgrounds.