PERTURBATIONS OF THE ROBERTSON-WALKER SPACE - MULTICOMPONENT SOURCES AND GENERALIZED GRAVITY

We present cosmological perturbation equations in the Robertson-Walker background space, considering multicomponent fluid sources with interactions between them. We generalize the perturbation equations applicable to a class of generalized gravity theories with multicomponent fluids and fields as sources. Equations are derived from the covariant equations and presented, following Bardeen's recent suggestion, using the raw kinematic variables of the normal frame with an unspecified gauge. In this way, the equations are easily adaptable to various gauge conditions and also to various gauge-invariant formulations. Relations between different gauges and also to the gauge-invariant formulations are explained. Since the energy-momentum tensor of the fluid part is separately conserved even in the generalized gravity theories, the component equations follow from the conservation equations of each component. We present separately the vorticity and the gravitational wave perturbation equations in the generalized gravity theories with multicomponent sources. Although we discuss various aspects of the cosmological perturbations, the main concern is the new formulation of perturbation equations applicable to a broad range of generalized gravity theories, including general relativistic formulation with multicomponent sources.