Magnetohydrodynamics in the Early Universe and the Damping of Non-linear Alfvén Waves

The evolution and viscous damping of cosmic magnetic fields in the early universe, is analysed. Using the fact that the fluid, electromagnetic, and shear viscous energy-momentum tensors are all conformally invariant, the evolution is transformed from the expanding universe setting into that in flat spacetime. Particular attention is paid to the evolution of nonlinear Alfvén modes. For a small enough magnetic field, which satisfies our observational constraints, these wave modes either oscillate negligibly or, when they do oscillate, become overdamped. Hence they do not suffer Silk damping on galactic and subgalactic scales. The smallest scale which survives damping depends on the field strength and is of order a dimensionless Alfvén velocity times the usual baryon-photon Silk damping scale. After recombination, nonlinear effects can convert the Alfvén mode into compressional, gravitationally unstable waves and seed cosmic structures if the cosmic magnetic field is sufficiently strong.