Strong coupling in massive gravity by direct calculation

TL;DR

The paper addresses the strong coupling problem in four-dimensional massive gravity with the Fierz-Pauli mass term. It directly verifies the strong-coupling scale $\Lambda = (M_{Pl}^2 m^4)^{1/5}$ by computing the 2→2 scattering amplitude of longitudinal gravitons and the one-loop graviton propagator in flat space. It finds that the high-energy amplitude scales as ${\cal M} \sim \frac{E^{10}}{\Lambda^{10}}$ after cancellations, and that the one-loop correction to the propagator becomes comparable to the tree-level term at $E \sim \Lambda$, confirming $\Lambda$ as the strong coupling scale. These results support the necessity of new physics or modifications (e.g., Lorentz-violating terms) to achieve a phenomenologically viable theory of massive gravity.

Abstract

We consider four-dimensional massive gravity with the Fierz-Pauli mass term. The analysis of the scalar sector has revealed recently that this theory becomes strongly coupled above the energy scale Λ= (M_{Pl}^2 m^4)^{1/5} where m is the mass of the graviton. We confirm this scale by explicit calculations of the four-graviton scattering amplitude and of the loop correction to the interaction between conserved sources.

Figures (3)

• Figure 1: Scattering through the four point vertex.
• Figure 2: Scattering via the s-, t- and u-channel exchange.
• Figure 3: Graviton propagator at one loop.