On the 6th Mode in Massive Gravity

TL;DR

This paper demonstrates that massive gravity models with six degrees of freedom can be stable and ghost-free due to background pressure effects, challenging previous beliefs about inherent instabilities.

Contribution

It shows that massive gravity models with six degrees of freedom are stable and ghost-free when considering the medium interpretation and background effects.

Findings

Stable phonon-like excitations in the medium

No ghost-like instabilities across wavelengths

Stability confirmed on expanding Universe

Abstract

Generic massive gravity models in the unitary gauge correspond to a self-gravitating medium with six degrees of freedom. It is widely believed that massive gravity models with six degrees of freedom have an unavoidable ghost-like instability; however, the corresponding medium has stable phonon-like excitations. The apparent contradiction is solved by the presence of a non-vanishing background pressure and energy density of the medium that opens up a stability window. The result is confirmed by looking at linear stability on an expanding Universe, recovering the flat space stability conditions in the small wavelength limit. Moreover, one can show that under rather mild conditions, no ghost-like instability is present for any wavelength. As a result, exploiting the medium interpretation, a generic massive gravity model with six degrees of freedom is perfectly viable.