Plasma electrodynamics in the expanding Universe

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Abstract
The 3+1 formalism of Thorne and Macdonald is used to formulate the electrodynamic equations for a plasma in a spatially flat Robertson-Walker metric. The conformal flatness of this space-time ensures that these equations closely mirror those of flat space-time. The linearized Vlasov-Maxwell equations are solved for the case of an unmagnetized plasma of ultrarelativistic particles and antiparticles, and the results are compared with those of classical kinetic theory and quantum field theory in special relativity. The Vlasov-Maxwell equations for a plasma of nonrelativistic particles are not conformally invariant, so a fluid approximation is used to obtain the linear modes of oscillation, again for an unmagnetized plasma. The plasma modes redshift at rates which depend on the rate of expansion of the Universe, and whether the electromagnetic fields or the particles dominate the dynamics.