Covariant constraints in ghost free massive gravity

TL;DR

This paper presents a covariant, vielbein-based reformulation of ghost-free massive gravity that simplifies the counting of constraints and clarifies the conditions needed to eliminate the Boulware-Deser ghost.

Contribution

It introduces a covariant vielbein approach to identify constraints in massive gravity and highlights a subset of theories where the ghost is naturally absent.

Findings

Simplified covariant constraint counting method

Identification of a subset of ghost-free theories

New approach to extract kinetic terms for additional polarizations

Abstract

We show that the reformulation of the de Rham-Gabadadze-Tolley massive gravity theory using vielbeins leads to a very simple and covariant way to count constraints, and hence degrees of freedom. Our method singles out a subset of theories, in the de Rham-Gabadadze-Tolley family, where an extra constraint, needed to eliminate the Boulware Deser ghost, is easily seen to appear. As a side result, we also introduce a new method, different from the Stuckelberg trick, to extract kinetic terms for the polarizations propagating in addition to those of the massless graviton.