Cosmological Perturbation Theory With Background Anisotropic Curvature

The theory of cosmological perturbations is extended to spacetimes displaying isotropic expansion but anisotropic curvature. The perturbed Einstein equation and Boltzmann equations for massless and massive particles are derived in a general gauge and a decomposition of perturbations into harmonic modes and moments is proposed. Generalization to the case where anisotropic expansion is also present in the background is discussed.