Weakly-coupled metastable graviton

TL;DR

This paper investigates the interactions of a massive graviton's polarizations in the DGP model, proposing a new perturbation approach that maintains tractability and aligns with General Relativity at observable scales.

Contribution

It introduces constrained perturbation theory to address perturbative breakdowns in the DGP model, enabling consistent analysis of graviton polarizations.

Findings

Couplings of extra polarizations are suppressed at sub-horizon scales.

The model aligns with General Relativity at observable distances.

Deviations from GR appear at the horizon scale.

Abstract

A graviton of a nonzero mass and decay width propagates five physical polarizations. The question of interactions of these polarizations is crucial for viability of models of massive/metastable gravity. This question is addressed in the context of the DGP model of a metastable graviton. First, I argue that the well-known breakdown of a naive perturbative expansion at a low scale is an artifact of the weak-field expansion itself. Then, I propose a different expansion -- the constrained perturbation theory -- in which the breakdown does not occur and the theory is perturbatively tractable all the way up to its natural ultraviolet cutoff. In this approach the couplings of the extra polarizations to matter and their selfcouplings appear to be suppressed and should be neglected in measurements at sub-horizon scales. The model reproduces results of General Relativity at observable distances with high accuracy, while predicting deviations from them at the present-day horizon scale.