Nonlinear partially massless from massive gravity?

We show that consistent nonlinear partially massless models cannot be obtained starting from “f-g” massive gravity, with “f” the embedding de Sitter space. The obstruction, which is also the source of f-g acausality, is the very same fifth constraint that removes the notorious sixth ghost excitation. Here, however, it blocks extension of the gauge invariance (appearing for mass to de Sitter cosmological constant tunings) that removed the helicity-zero mode at linear level. Separately, our methods allow us to almost complete the proof that all f-g models are acausal