Cosmological Stability Bound in Massive Gravity and Bigravity
  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.
