Ghost-free Massive Gravity with a General Reference Metric

TL;DR

This paper extends ghost-free massive gravity theories to include a general reference metric, proving their consistency and potential to describe massive spin-2 fields in arbitrary backgrounds.

Contribution

It generalizes the proof of ghost freedom from flat to arbitrary reference metrics in non-linear massive gravity theories.

Findings

Existence of a Hamiltonian constraint eliminating the Boulware-Deser ghost.

Extension of ghost-free conditions to general reference metrics.

Potential application to massive spin-2 fields in arbitrary backgrounds.

Abstract

Theories of massive gravity inevitably include an auxiliary reference metric. Generically, they also contain an inconsistency known as the Boulware-Deser ghost. Recently, a family of non-linear massive gravity actions, formulated with a flat reference metric, were proposed and shown to be ghost free at the complete non-linear level. In this paper we consider these non-linear massive gravity actions but now formulated with a general reference metric. We extend the proof of the absence of the Boulware-Deser ghost to this case. The analysis is carried out in the ADM formalism at the complete non-linear level. We show that in these models there always exists a Hamiltonian constraint which, with an associated secondary constraint, eliminates the ghost. This result considerably extends the range of known consistent non-linear massive gravity theories. In addition, these theories can also be used to describe a massive spin-2 field in an arbitrary, fixed gravitational background. We also discuss the positivity of the Hamiltonian.