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

TL;DR

This paper analyzes the Ogievetsky-Polubarinov massive gravity theory, revealing conditions under which it remains stable and ghost-free, especially in de Sitter space, and compares it to modern ghost-free models.

Contribution

It demonstrates that the original OP massive gravity theory can be stable in de Sitter space and identifies conditions where the Boulware-Deser mode is benign, connecting historical and modern models.

Findings

De Sitter space remains stable for large Hubble rates.

The theory propagates 6 degrees of freedom but can be ghost-free in certain regimes.

The Milne universe is stable in the UV limit.

Abstract

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.