The Ogievetsky-Polubarinov massive gravity and the benign Boulware-Deser mode

We present our analysis of the theory constructed in 1965 by Ogievetsky and Polubarinov (OP)— the first ever theory of interacting massive gravitons. Its mass term is adjusted in such a way that the non-linear field equations imply as a consequence the linear Hilbert-Lorentz condition, which restricts the spin of states in the theory. Strikingly, for special parameter values this theory coincides with one of the "ghost-free" massive gravity models rediscovered only in 2010. For generic parameter values, however, it propagates 6 degrees of freedom and shows ghost around flat space. Surprizingly, we find that the de Sitter space remains stable for a large region of the parameter space, provided that the Hubble expansion rate is large enough, hence the Boulware-Deser mode is benign in this case. We study also other solutions and find that the Milne universe— a sector of Minkowski space—is stable in the UV limit. This presumably implies that at the non-linear level the ghost instability in flat space develops only for long waves, similarly to the classical Jeans instability.