Ghost‐Free Completion of An Effective Matter Coupling in Bimetric Theory.

Abstract: We consider a particular set of ghost‐free interactions for three spin‐2 fields in which we freeze out the dynamics of the metric tensor that couples to the matter sector. Integrating out the non‐dynamical degrees of freedom in vacuum results in a ghost‐free bimetric theory. In the presence of the matter source, which we treat as a small perturbation, the equations for the non‐dynamical field can be solved perturbatively for its vierbein. This results in ghost‐free bimetric theory in vierbein formulation with a modified matter coupling. To lowest order in matter perturbations, we precisely obtain an effective matter coupling that has been suggested earlier in the literature. This coupling contains a linear combination of the two vierbeine whose corresponding metric fluctuation coincides with the massless spin‐2 mode. In the past, bimetric theory with this symmetric coupling has been treated as an effective theory valid at low energies without a ghost‐free completion. Our results demonstrate that the effective matter coupling can be rendered entirely ghost‐free by including the higher‐order corrections obtained from the trimetric setup. [ABSTRACT FROM AUTHOR]