Ghosts, Strong Coupling and Accidental Symmetries in Massive Gravity

TL;DR

Massive gravity exhibits a vDVZ discontinuity that is cured by a Vainshtein mechanism at $r_V=(GM/m^4)^{1/5}$. The authors show that the strong coupling of the scalar mode can be reformulated as propagation of a ghost with scale $\Lambda=(M_P m^4)^{1/5}$, linking strong coupling to the BD ghost. Inside $r_V$, ghost exchange cancels the vDVZ attraction, yielding a perturbative two-field description; outside, one can use the original higher-derivative scalar formulation. The work contrasts with DGP and deconstructed gravity, clarifying where ghosts are needed for screening and where they are not, and highlighting the role of accidental symmetries and nonlinearities in IR modifications of gravity.

Abstract

We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghost-like degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbatively, while at larger distances one can use the higher derivative formulation. We also compare massive gravity with other models, namely deconstructed theories of gravity, as well as DGP model. In the latter case we argue that the Vainshtein recovery process is of different nature, not involving a ghost degree of freedom.