  We propose and develop a general algorithm for finding the action for
cosmological perturbations which rivals the conventional, gauge-invariant
approach and can be applied to theories with more than one metric. We then
apply it to a particular case of bigravity, focusing on the Eddington- inspired
Born-Infeld theory, and show that we can obtain a nearly scale-invariant power
spectrum for both scalar and tensor primordial quantum perturbations.
Unfortunately, in the case of the minimal Eddington-inspired Born-Infeld
theory, we find that the tensor-to-scalar ratio of perturbations is
unacceptably large. We discuss the applicability of our general method and the
possibility of resurrecting the specific theory we have looked at.
