Resummation of Massive Gravity

TL;DR

This paper develops ghost-free, covariant non-linear massive gravity theories that resum all nonlinear terms and maintain Hamiltonian constraints up to quartic order, extending to all orders in a toy model.

Contribution

It constructs explicit all-order resummed non-linear massive gravity theories that are ghost-free in the decoupling limit and preserve Hamiltonian constraints beyond linear order.

Findings

Ghost-free in the decoupling limit to all orders

Hamiltonian constraint maintained up to quartic order

Results extended to a toy model to all orders

Abstract

We construct four-dimensional covariant non-linear theories of massive gravity which are ghost-free in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an effective field theory of massive gravity. We show that away from the decoupling limit the Hamiltonian constraint is maintained at least up to and including quartic order in non-linearities, hence, excluding the possibility of the Boulware-Deser ghost up to this order. We also show that the same remains true to all orders in a similar toy-model.