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.

Latex, 19 pages

References in corpus (12)

• Generalization of the Fierz-Pauli Action
• Bimetric Gravity from Ghost-free Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• On Non-Linear Actions for Massive Gravity
• Interacting Spin-2 Fields
• On couplings to matter in massive (bi-)gravity
• The coupling to matter in Massive, Bi- and Multi-Gravity
• Particular Solutions in Bimetric Theory and Their Implications
• The Boulware-Deser mode in Zwei-Dreibein gravity
• Metric Formulation of Ghost-Free Multivielbein Theory
• Perturbations for massive gravity theories

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