Behavior of higher modes of gravitational waves and gauge-invariant density perturbations in Bianchi IX cosmological models
The behavior of higher modes of gravitational waves is investigated in a Bianchi IX model, and an asymptotic analysis is performed for large values of the intrinsic magnetic quantum number of the angular momentum operator. The asymptotic equations fit naturally into the theory of the quantum motions of the rigid rotor. To investigate the interaction of gravitational waves and density perturbations, a gauge-invariant density perturbation is constructed using the expansion of the gauge vector in Wigner functions. This extension of perturbations to anisotropic backgrounds may shed light on some cosmological problems.