Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory

Some formulae for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe, which is developed in the papers [K.Nakamura, Prog.Theor.Phys., 117 (2007), 17.]. We derive the formulae for the perturbations of the energy momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a signle scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing.