Absence of ghost in a new bimetric-matter 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.