Resolving the Ghost Problem in non-Linear Massive Gravity

TL;DR

This paper demonstrates that a class of non-linear massive gravity models can be free of the Boulware-Deser ghost at all orders, establishing a consistent theory of massive gravity in four dimensions.

Contribution

It proves the Hamiltonian constraint persists non-linearly and suggests a secondary constraint, ensuring ghost freedom in these models.

Findings

Hamiltonian constraint maintained at non-linear level

Existence of a secondary constraint argued for

Boulware-Deser ghost eliminated to all orders

Abstract

We analyze the ghost issue in the recently proposed models of non-linear massive gravity in the ADM formalism. We show that, in the entire two-parameter family of actions, the Hamiltonian constraint is maintained at the complete non-linear level and we argue for the existence of a non-trivial secondary constraint. This implies the absence of the pathological Boulware-Deser ghost to all orders. To our knowledge, this is the first demonstration of the existence of a consistent theory of massive gravity at the complete non-linear level, in four dimensions.