Magnetized plasmas in the early universe

The fluid equations governing a magnetized plasma in a spatially flat Friedmann-Robertson-Walker metric are formulated using the 3+1 formalism of Thorne and MacDonald. They are the generalization of our previous work for a zero external field. These equations are first solved in the ultrarelativistic limit where the electron-positron plasma is treated. The equations turn out to be conformally invariant, so that the results closely resemble those of flat spacetime. The nonrelativistic limit is then studied in both the matter- and radiation-dominated eras. Here it is found that the various magnetoplasma modes redshift at different rates, and are governed by the rate of expansion of the Universe as well as whether the dynamics are dominated by matter or radiation.