  The theory of bigravity offers one of the simplest possibilities to describe
a massive graviton while having self-accelerating cosmological solutions
without a cosmological constant. However, it has been shown recently that
bigravity is affected by early-time fast growing modes on the tensor sector.
Here we argue that we can only trust the linear analysis up to when
perturbations are in the linear regime and use a cut-off to stop the growing of
the metric perturbations. This analysis, although more consistent, still leads
to growing tensor modes that are unacceptably large for the theory to be
compatible with measurements of the cosmic microwave background (CMB), both in
temperature and polarization spectra. In order to suppress the growing modes
and make the model compatible with CMB spectra, we find it necessary to either
fine-tune the initial conditions, modify the theory or set the cut-off for the
tensor perturbations of the second metric much lower than unity. Initial
conditions such that the growing mode is sufficiently suppresed can be achieved
in scenarios in which inflation ends at the GeV scale.
