General-relativistic plasma physics in the early Universe

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Abstract
We apply the ‘‘3+1’’ formalism of Thorne and Macdonald to construct the linearized theory of a general-relativistic electron-positron plasma in the early Universe. Close formal correspondence between the theory of such plasmas and that of their special-relativistic counterparts is demonstrated. The time variation of the plasma modes due to the expansion of the background is determined for the case of a radiation-dominated Universe; it is found that the frequencies of the basic modes redshift like the frequency of a free photon. A simple kinetic argument is used to justify the neglect of creation and annihilation (collisional) effects. The formulation is sufficiently straightforward to be readily amenable to numerical implementation. Our results can be applied to the study of the origin of primordial intergalactic magnetic fields, as well as to the problem of matter fluctuations in the early Universe.