Cosmology of bigravity with doubly coupled matter
  We study cosmology in the bigravity formulation of the dRGT model where
matter couples to both metrics. At linear order in perturbation theory two mass
scales emerge: an hard one from the dRGT potential, and an environmental
dependent one from the coupling of bigravity with matter. At early time, the
dynamics is dictated by the second mass scale which is of order of the Hubble
scale. The set of gauge invariant perturbations that couples to matter follow
closely the same behaviour as in GR. The remaining perturbations show no issue
in the scalar sector, while problems arise in the tensor and vector sectors.
During radiation domination, a tensor mode grows power-like at super-horizon
scales. More dangerously, the only propagating vector mode features an
exponential instability on sub-horizon scales. We discuss the consequences of
such instabilities and speculate on possible ways to deal with them.
