On couplings to matter in massive (bi-)gravity

TL;DR

This work analyzes how matter couplings influence the ghost-free structure of ghost-free massive gravity and bi-gravity. It shows that covariant coupling to a single metric preserves the ghost-free potential at one loop, while direct coupling to both metrics reintroduces a BD ghost classically and detunes the potential at a low scale quantum mechanically. To address this, the authors introduce a composite effective metric g_eff built from both metrics, demonstrating ghost freedom in several limits (including mini-superspace and decoupling limit) and showing that exact FLRW solutions can exist without BD ghosts, though a full ADM analysis reveals a ghost on generic backgrounds. The results map a nuanced landscape of viable matter couplings, with a promising but constrained path toward cosmologically interesting scenarios within an effective field theory framework that remains healthy below a cutoff above the strong coupling scale.

Abstract

We investigate the coupling to matter in ghost-free massive (bi-)gravity. When species in the matter sector couple covariantly to only one metric, we show that at one--loop these couplings do not spoil the special structure of the graviton potential. When the same species couples directly to both metrics we show that a ghost is present at the classical level and that loops destroy the special structure of the potential at an unacceptably low scale. We then propose a new `composite' effective metric built out of both metrics. When matter fields couple covariantly to this effective metric, the would be Boulware--Deser ghost is absent in different representative limits. At one--loop such couplings do not detune the special structure of the potential. We conjecture that matter can couple covariantly to that effective metric in all generality without introducing any Boulware--Deser ghost below a cut-off scale parametrically larger than the strong coupling scale. We also discuss alternative couplings to matter where the kinetic and potential terms of the matter field couple to different metrics. In both cases we discuss preliminary implications for cosmology.