Instability in a minimal bimetric gravity model

We discuss in detail a particularly simple example of a bimetric massive gravity model which seems to offer an alternative to the standard cosmological model at background level. For small redshifts, its equation of state is $w(z)\approx-1.22_{-0.02}^{+0.02}-0.64_{-0.04}^{+0.05}z/(1+z)$. Just like $\Lambda$CDM, it depends on a single parameter, has an analytical background expansion law and fits the expansion cosmological data well. However, confirming previous results, we find that the model is unstable at early times at small scales and speculate over possible ways to cure the instability. In the regime in which the model is stable, we find that it fits the linear perturbation observations well and has a growth index of approximately $\gamma=0.47$.