Self-accelerating Massive Gravity: Covariant Perturbation Theory

TL;DR

This paper provides a comprehensive covariant analysis of quadratic perturbations in massive gravity, clarifying the propagation of degrees of freedom and resolving previous discrepancies in the literature.

Contribution

It offers a complete covariant framework for quadratic perturbations in massive gravity around isotropic self-accelerating backgrounds, revealing the full kinetic structure.

Findings

3 of 4 Stuckelberg modes propagate alongside 2 tensor modes

Kinetic structure appears at order in graviton mass, including curvature effects

Resolves discrepancies in previous literature regarding degrees of freedom

Abstract

We undertake a complete and covariant treatment for the quadratic Lagrangian of all of the degrees of freedom of massive gravity with a fixed flat fiducial metric for arbitrary massive gravity parameters around any isotropic self-accelerating background solution. Generically, 3 out of 4 Stuckelberg degrees of freedom propagate in addition to the usual 2 tensor degrees of freedom of general relativity. The complete kinetic structure typically is only revealed at an order in the graviton mass that is equivalently to retaining curvature terms in a locally flat expansion. These results resolve several apparent discrepancies in the literature where zero degrees of freedom propagate in either special cases or approximate treatments as well as decoupling limit analyses which attempt to count longitudinal degrees of freedom.