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Some formulae for the perturbations of the matter fields are summarizedwithin the framework of the second-order gauge-invariant cosmologicalperturbation theory in a four dimensional homogeneous isotropic universe, whichis developed in the papers [K.Nakamura, Prog.Theor.Phys., 117 (2007), 17.]. Wederive the formulae for the perturbations of the energy momentum tensors andequations of motion for a perfect fluid, an imperfect fluid, and a signlescalar field, and show that all equations are derived in terms ofgauge-invariant variables without any gauge fixing.

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