Absence of ghost in a new bimetric-matter coupling

TL;DR

This paper demonstrates through nonlinear Hamiltonian analysis that a recently proposed new matter coupling in bimetric theory does not reintroduce the Boulware-Deser ghost, ensuring the theory remains consistent.

Contribution

It provides a nonlinear Hamiltonian analysis showing the new matter coupling is ghost-free, using variables connecting metric and vielbein formulations.

Findings

The new matter coupling does not reduce the number of constraints.

It does not reintroduce the Boulware-Deser ghost.

The analysis confirms the ghost-free nature of the coupling.

Abstract

Interactions in bimetric theory, which can describe gravity in the presence of an extra spin-2 field, are severely constrained by the requirement of the absence of the Boulware-Deser ghost instability. Recently an interesting new matter coupling was proposed in terms of a composite metric but it was claimed to reintroduce the ghost. In this paper we carry out a nonlinear Hamiltonian analysis of this new matter coupling and show that it is indeed ghost-free. The analysis involves using a new set of variables that naturally appear in the relation between the metric and vielbein formulations of bimetric theory. In terms of these variables we show that the new matter coupling does not reduce the number of constraints in bimetric theory and hence does not reintroduce the Boulware-Deser ghost.