Nonlinear , ghost-free massive gravity has two tensor fields ; when both are dynamical , the mass of the graviton can lead to cosmic acceleration that agrees with background data , even in the absence of a cosmological constant .
Here the question of the stability of linear perturbations in this bimetric theory is examined .
Instabilities are presented for several classes of models , and simple criteria for the cosmological stability of massive bigravity are derived .
In this way , we identify a particular self-accelerating bigravity model , infinite-branch bigravity ( IBB ) , which exhibits both viable background evolution and stable linear perturbations .
We discuss the modified gravity parameters for IBB , which do not reduce to the standard \Lambda CDM result at early times , and compute the combined likelihood from measured growth data and type Ia supernovae .
IBB predicts a present matter density \Omega _ { m 0 } = 0.18 and an equation of state w ( z ) = -0.79 + 0.21 z / ( 1 + z ) .
The growth rate of structure is well-approximated at late times by f ( z ) \approx \Omega _ { m } ^ { 0.47 } [ 1 + 0.21 z / ( 1 + z ) ] .
The implications of the linear instability for other bigravity models are discussed : the instability does not necessarily rule these models out , but rather presents interesting questions about how to extract observables from them when linear perturbation theory does not hold .