Massive Gravity Coupled to Galileons is Ghost-Free

It is possible to couple Dirac-Born-Infeld scalars possessing generalized Galilean internal shift symmetries (Galileons) to nonlinear massive gravity in four dimensions, in such a manner that the interactions maintain the Galilean symmetry. Such a construction is of interest, because it is not possible to couple such fields to massless general relativity in the same way. We show that this theory has the primary constraint necessary to eliminate the Boulware-Deser ghost, thus preserving the attractive properties of both the Galileons and ghost-free massive gravity.