Sixth mode in massive gravity

Generic massive gravity models in the unitary gauge correspond to a self-gravitating medium with six degrees of freedom (d.o.f.). It is widely believed that massive gravity models with six d.o.f. have an unavoidable ghostlike instability; however, the corresponding medium has stable phononlike excitations. The apparent contradiction is solved by the presence of a nonvanishing background pressure and energy density of the medium that opens up a stability window. The result is confirmed by looking at linear stability on an expanding Universe, recovering the flat space stability conditions in the small wavelength limit. Moreover, one can show that under rather mild conditions, no ghostlike instability is present for any wavelength. As a result, exploiting the medium interpretation, a generic massive gravity model with six d.o.f. is perfectly viable.