Cosmological Stability Bound in Massive Gravity and Bigravity

TL;DR

The work derives a cosmological stability bound on the graviton mass for spatially flat FRW setups in massive gravity and bigravity, obtained from requiring a positive kinetic term for the helicity-0 mode. It provides two independent derivations—the minisuperspace and the $ ext{Lambda}_3$ decoupling-limit approach—and shows that FRW solutions in massive gravity with an FRW reference metric are ruled out by a Higuchi–Vainshtein tension, while bigravity can resolve this tension and support self-accelerating cosmologies. A key result is the generalized bound in bigravity, $ ilde{m}^2(H)ig(H^2+H_f^2 M_p^2/M_f^2ig)\,\ge 2H^4$, which enables viable cosmologies when the reference metric is dynamical. The decoupling-limit analysis uncovers a dual Galileon structure relating the helicity-0 mode to a dual field $ ho$, and demonstrates that vector modes remain stable under the bound; the study also argues against the existence of nonlinear partially massless (PM) gravity within these models.

Abstract

We give a simple derivation of a cosmological bound on the graviton mass for spatially flat FRW solutions in massive gravity with an FRW reference metric and for bigravity theories. This bound comes from the requirement that the kinetic term of the helicity zero mode of the graviton is positive definite. The bound is dependent only on the parameters in the massive gravity potential and the Hubble expansion rate for the two metrics. We derive the decoupling limit of bigravity and FRW massive gravity, and use this to give an independent derivation of the cosmological bound. We recover our previous results that the tension between satisfying the Friedmann equation and the cosmological bound is sufficient to rule out all observationally relevant FRW solutions for massive gravity with an FRW reference metric. In contrast, in bigravity this tension is resolved due to different nature of the Vainshtein mechanism. We find that in bigravity theories there exists an FRW solution with late time self-acceleration for which the kinetic terms for the helicity-2, helicity-1 and helicity-0 are generically nonzero and positive making this a compelling candidate for a model of cosmic acceleration. We confirm that the generalized bound is saturated for the candidate partially massless (bi)gravity theories but the existence of helicity-1/helicity-0 interactions implies the absence of the conjectured partially massless symmetry for both massive gravity and bigravity.