  In this paper we study gravitational wave perturbations in a cosmological
setting of bigravity which can reproduce the {\Lambda}CDM background and large
scale structure. We show that in general gravitational wave perturbations are
unstable and only for very fine tuned initial conditions such a cosmology is
viable. We quantify this fine tuning. We argue that similar fine tuning is also
required in the scalar sector in order to prevent the tensor instability to be
induced by second order scalar perturbations. Finally, we show that due to this
power law instability, models of bigravity can lead to a large tensor to scalar
ratio even for low scale inflation.
