Magnetohydrodynamics in the expanding Universe

We present a comprehensive study of the magnetohydrodynamic (MHD) modes and corresponding state eigenvectors in the early Universe. The fluid equations are formulated using the 3+1 formalism of Thorne and MacDonald, as utilized by us in our previous work. The equations are then solved in various regimes. The first of these is the ultrarelativistic limit where we study the electron-positron plasma at high temperatures. Here, we find the conformal invariance property of the metric ensures results very similar to those of flat spacetime. We also investigate an electron-proton fluid before and after recombination where a nonrelativistic limit suffices. Here the various frequencies redshift at different rates with respect to one another, which complicates the solutions considerably. A thorough discussion, both quantitative and qualitative is given for all solutions obtained. {} 1995 The American Physical Society.