Bimetric Gravity from Ghost-free Massive Gravity

TL;DR

This paper introduces a novel ghost-free bimetric gravity theory where both metrics are dynamical, extending previous massive gravity models and maintaining consistency without the Boulware-Deser ghost.

Contribution

It presents the first consistent non-linear bimetric gravity theory with both metrics dynamical, free of the Boulware-Deser ghost, building on ghost-free massive gravity models.

Findings

Successfully formulated a ghost-free bimetric theory with two dynamical metrics.

Demonstrated the absence of Boulware-Deser ghost in the new theory.

Extended the class of consistent non-linear gravity theories.

Abstract

Generically, non-linear bimetric theories of gravity suffer from the same Boulware-Deser ghost instability as non-linear theories of massive gravity. However, recently proposed theories of massive gravity have been shown to be ghost-free. These theories are formulated with respect to a flat, non-dynamical reference metric. In this work we show that it is possible to give dynamics to the reference metric in such a way that the consistency of the theory is maintained. The result is a non-linear bimetric theory of a massless spin-2 field interacting with a massive spin-2 field that is free of the Boulware-Deser ghost. To our knowledge, this is the first construction of such a ghost-free bimetric theory.