Gravitational- and self-coupling of partially massless spin 2

We show that higher spin systems specific to cosmological spaces are subject to the same problems as models with Poincar\'e limits. In particular, we analyze partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual background- and self-coupling difficulties: Consistent free field propagation does not extend beyond background Einstein geometries. Then (using conformal, Weyl, gravity, which contains relative ghost PM and graviton excitations) we find that avoiding graviton ghosts restricts Weyl-generated PM self-couplings to the usual, leading, safe, Noether current cubic ones.