On the evolution of linear waves in cosmological plasmas

The scalings for basic plasma modes in the Friedmann-Robertson-Walker model of the expanding Universe are revised. Contrary to the existing literature, the wave collisionless evolution must comply with the action conservation theorem. The proper steps to deduce the action conservation from ab initio analytical calculations are presented, and discrepancies in the earlier papers are identified. In general, the cosmological wave evolution is more easily derived from the action conservation in the collisionless limit, whereas when collisions are essential, the statistical description must suffice, thereby ruling out the need for using dynamic equations in either case.