Strong Coupling and Bounds on the Graviton Mass in Massive Gravity

TL;DR

This paper derives bounds on the graviton mass in massive gravity theories, showing that to remain perturbative at millimeter scales, the graviton mass must be above roughly 1 meV, conflicting with general relativity at cosmological scales.

Contribution

It provides new bounds on the graviton mass based on perturbativity constraints at short distances, considering environmental effects and extensions like Galileon theories.

Findings

Graviton mass must be >~1 meV for perturbativity at 1 mm scale

Bounds are weaker with fine-tuning but still significant

Results extend to quartic and quintic Galileon theories

Abstract

The theory of a single massive graviton has a cutoff much below its Planck scale, because the extra modes from the graviton multiplet involve higher derivative self-interactions, controlled by a scale convoluted from the small graviton mass. Generically, these correct the propagator by environmental effects. The resulting effective cutoff depends on the environmental parameters and the graviton mass. Requiring the theory to be perturbative down to ${\cal O}(1) mm$, we derive bounds on the graviton mass, corresponding to $\gtrsim {\cal O}(1) meV$ for the generic case, and somewhat weaker bounds in cases of fine-tuning. In all cases the mass is required to be much too large for the theory to conform with GR at cosmological distances. Similar results also hold in quartic and quintic Galileon theory.