Cosmological Stability Bound in Massive Gravity and Bigravity

TL;DR

This paper derives a cosmological bound on the graviton mass in massive gravity and bigravity theories, showing how it impacts the viability of FRW solutions and the potential for cosmic acceleration.

Contribution

It provides a simple derivation of the cosmological stability bound and analyzes its implications for massive gravity and bigravity models, including the existence of self-accelerating solutions.

Findings

The bound depends only on potential parameters and Hubble rate.

Massive gravity solutions are ruled out by the bound, but bigravity can satisfy it.

Bigravity admits self-accelerating FRW solutions with positive kinetic terms.

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.