Perturbations of an anisotropic spacetime: Formulation

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Abstract
We present a formulation for studying the evolution of perturbations in an anisotropic model universe. The formulation is designed to allow the systematic study of the evolution of perturbations in the spatially homogeneous and anisotropic Bianchi type-I spacetime. The spatial anisotropy in the background causes the couplings of the density perturbation mode with the gravitational wave and the rotation to the linear order. Our formulation includes the imperfect fluid terms in the background and the perturbations, and the cosmological constant in the background. We use the complete set of perturbed equations without fixing gauge mode. After resolving the gauge issue we present the equations so that we can use the advantage of having the gauge freedom efficiently, i.e., in a gauge ready form. The formulation is extended so that it can treat the system of multicomponents.