Strong Coupling and Bounds on the Graviton Mass in Massive Gravity

TL;DR

This work analyzes the environmental strong-coupling problem in massive gravity theories, focusing on the dRGT framework and its decoupling limit. By constructing an Earth-background effective theory and diagonalizing the kinetic mixings, the authors determine the terrestrial strong-coupling scale, finding that perturbativity down to 1 mm requires a graviton mass much larger than the Hubble scale. Generic bounds place m at least around 1 meV, with fine-tuned scenarios weakening the bound to as low as ~10^{-15} eV, but in all cases cosmological GR cannot be recovered. The study further shows that cubic, quartic, and quintic Galileon theories exhibit analogous strong-coupling behavior, indicating a common obstacle to achieving cosmic acceleration while maintaining predictivity at short scales.

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.