Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity

TL;DR

This paper confirms the existence of a secondary constraint in non-linear massive and bimetric gravity theories, ensuring the absence of the Boulware-Deser ghost and validating their theoretical consistency.

Contribution

It explicitly demonstrates the secondary constraint in these theories, providing a rigorous proof of ghost absence in non-linear massive and bimetric gravity.

Findings

Secondary constraint is explicitly demonstrated.

Boulware-Deser ghost is absent in these theories.

Theories are shown to be free of ghost-related instabilities.

Abstract

In massive gravity and in bimetric theories of gravity, two constraints are needed to eliminate the two phase-space degrees of freedom of the Boulware-Deser ghost. For recently proposed non-linear theories, a Hamiltonian constraint has been shown to exist and an associated secondary constraint was argued to arise as well. In this paper we explicitly demonstrate the existence of the secondary constraint. Thus the Boulware-Deser ghost is completely absent from these non-linear massive gravity theories and from the corresponding bimetric theories.