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 $\mathrm{\Lambda }\mathrm{CDM}$ result at early times, and compute the combined likelihood from measured growth data and type Ia supernovae. IBB predicts a present matter density ${\mathrm{\Omega }}_{m0}=0.18$ and an equation of state $w(z)=-0.79+0.21z/(1+z)$. The growth rate of structure is well approximated at late times by $f(z)\approx {\mathrm{\Omega }}_m^{0.47}[1+0.21z/(1+z)]$. 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.

• Received 7 August 2014

DOI:https://doi.org/10.1103/PhysRevD.90.124014