Helicity Decomposition of Ghost-free Massive Gravity

TL;DR

This paper performs a detailed helicity decomposition of ghost-free massive gravity, confirming the strong coupling scale at , clarifying misconceptions about lower energy scales, and deriving the Stueckelberg formalism without diffeomorphism invariance.

Contribution

It provides a comprehensive helicity decomposition of massive gravity, clarifies the true strong coupling scale, and shows how to derive the Stueckelberg formalism without relying on diffeomorphism invariance.

Findings

The strong coupling scale is , not lower scales like  or .

The number of propagating helicity modes remains five in the full nonlinear theory.

The Stueckelberg formalism can be derived from helicity decomposition without invoking diffeomorphism invariance.

Abstract

We perform a helicity decomposition in the full Lagrangian of the class of Massive Gravity theories previously proven to be free of the sixth (ghost) degree of freedom via a Hamiltonian analysis. We demonstrate, both with and without the use of nonlinear field redefinitions, that the scale at which the first interactions of the helicity-zero mode come in is $\Lambda_3=(M_Pl m^2)^{1/3}$, and that this is the same scale at which helicity-zero perturbation theory breaks down. We show that the number of propagating helicity modes remains five in the full nonlinear theory with sources. We clarify recent misconceptions in the literature advocating the existence of either a ghost or a breakdown of perturbation theory at the significantly lower energy scales, $\Lambda_5=(M_Pl m^4)^{1/5}$ or $\Lambda_4=(M_Pl m^3)^{1/4}$, which arose because relevant terms in those calculations were overlooked. As an interesting byproduct of our analysis, we show that it is possible to derive the Stueckelberg formalism from the helicity decomposition, without ever invoking diffeomorphism invariance, just from a simple requirement that the kinetic terms of the helicity-two, -one and -zero modes are diagonalized.