Massive Gravity: Exorcising the Ghost

TL;DR

The paper investigates nonlinear Boulware-Deser ghosts in Higgs-based massive gravity, showing the ghost reappears at fourth order away from the decoupling limit and is not simply tied to the Vainshtein scale. It analyzes nonlinear extensions and finds that ghost absence at a given order does not guarantee ghost-free behavior in the complete theory, unless one adopts Lorentz-violating modifications in the scalar sector. The authors illustrate that a two-degree-of-freedom massive graviton can be achieved with Lorentz-violating counterterms, but at the cost of breaking Lorentz invariance in field space. The work clarifies limitations in constructing consistent massive gravity theories and points to possible reformulations that reconcile diffeomorphism invariance with ghost freedom at relevant scales.

Abstract

We consider Higgs massive gravity [1,2] and investigate whether a nonlinear ghost in this theory can be avoided. We show that although the theory considered in [10,11] is ghost free in the decoupling limit, the ghost nevertheless reappears in the fourth order away from the decoupling limit. We also demonstrate that there is no direct relation between the value of the Vainshtein scale and the existence of nonlinear ghost. We discuss how massive gravity should be modified to avoid the appearance of the ghost.