Normal modes for metric fluctuations in a class of anisotropic backgrounds

We relax the assumption of isotropy of the background manifold in the gauge invariant approach to the theory of cosmological perturbations. We find the normal modes which diagonalize the perturbed action, for a scalar field minimally coupled to gravity in a manifold {\cal M} of the Bianchi-type I, under the assumption that the translations along an isotropic spatial subsection of {\cal M} are isometries of the full, perturbed background. We show that, in the absence of scalar field potential, the canonical variables for scalar and tensor metric perturbations satisfy exactly the same evolution equation.