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It is possible to couple Dirac-Born-Infeld (DBI) scalars possessinggeneralized Galilean internal shift symmetries (Galileons) to nonlinear massivegravity in four dimensions, in such a manner that the interactions maintain theGalilean symmetry. Such a construction is of interest because it is notpossible to couple such fields to massless General Relativity in the same way.We show that this theory has the primary constraint necessary to eliminate theBoulware-Deser ghost, thus preserving the attractive properties of both theGalileons and ghost-free massive gravity.

Massive gravity coupled to DBI Galileons is ghost free