Nonlinear massive gravity with additional primary constraint and absence of ghosts

We complete the Hamiltonian analysis of a specific model of nonlinear massive gravity that was started in 2012 [J. Kluson, J. High Energy Phys. 06 (2012) 170]. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism-invariant theory. Finally, we determine the number of physical degrees of freedom and we show that it corresponds to the number of physical modes of massive gravity.