Ghosts & Matter Couplings in Massive (bi-&multi-)Gravity

TL;DR

This paper clarifies the implications of a new matter coupling in ghost-free massive gravity, showing it reintroduces the Boulware-Deser ghost above the strong coupling scale but remains valid below the cut-off scale.

Contribution

It demonstrates that the new matter coupling removes the standard constraint, leading to ghost re-emergence, but remains consistent within a certain energy regime.

Findings

The standard constraint disappears with the new coupling on generic backgrounds.

The Boulware-Deser ghost reappears above the strong coupling scale.

The theory remains ghost-free in the decoupling limit below the cut-off.

Abstract

Recently, several works have investigated the coupling to matter in ghost-free massive (bi-&multi-)gravity and a new effective coupling to matter has been proposed. In this note we clarify some confusion on the existence and the implications of a ghost above the strong coupling scale. We confirm that the standard constraint which is otherwise typically present in this type of theories disappears on generic backgrounds as soon as this new coupling is considered. This implies the re-emergence of the Boulware-Deser ghost. Nevertheless the absence of ghost in the decoupling limit implies that the cut-off scale (if identified with the scale at which the ghost enters) is higher than the strong coupling scale. Therefore there is a valid interesting region of applicability for these couplings at scales below the cut-off.