Cutoff for Extensions of Massive Gravity and Bi-Gravity

TL;DR

This paper investigates the limits of extending ghost-free massive gravity theories, showing that most promising modifications introduce ghosts, and establishes an upper bound on the cutoff scale for these theories.

Contribution

It generalizes no-go theorems to vielbein formalism and demonstrates the presence of ghosts in extended models, setting bounds on their validity as effective field theories.

Findings

Most promising extensions contain a Boulware-Deser ghost.

A decoupling limit reveals ghosts in matter couplings and kinetic terms.

An upper bound on the cutoff scale for ghost-free extensions is established.

Abstract

Recently there has been interest in extending ghost-free massive gravity, bi-gravity, and multi-gravity by including non-standard kinetic terms and matter couplings. We first review recent proposals for this class of extensions, emphasizing how modifications of the kinetic and potential structure of the graviton and modifications of the coupling to matter are related. We then generalize existing no-go arguments in the metric language to the vielbein language in second-order form. We give an ADM argument to show that the most promising extensions to the kinetic term and matter coupling contain a Boulware-Deser ghost. However, as recently emphasized, we may still be able to view these extensions as effective field theories below some cutoff scale. To address this possibility, we show that there is a decoupling limit where a ghost appears for a wide class of matter couplings and kinetic terms. In particular, we show that there is a decoupling limit where the linear effective vielbein matter coupling contains a ghost. Using the insight we gain from this decoupling limit analysis, we place an upper bound on the cutoff for the linear effective vielbein coupling. This result can be generalized to new kinetic interactions in the vielbein language in second-order form. Combined with recent results, this provides a strong uniqueness argument on the form of ghost-free massive gravity, bi-gravity, and multi-gravity.