Magnetohydrodynamics in the Inflationary Universe

TL;DR

This paper analyzes magnetohydrodynamic waves in the early inflationary universe filled with a Zel'dovich fluid, revealing that wave behaviors resemble those in classical MHD but with unique features like superluminal group velocities.

Contribution

It provides a theoretical analysis of MHD wave modes during inflation, including their phase speeds and the behavior of Alfvén waves in a de Sitter universe.

Findings

Magnetosonic and Alfvén waves are similar to classical MHD modes.

Longitudinal magnetosonic wave is non-physical due to superluminal group velocity.

Alfvén velocity becomes negligible, indicating waves are frozen in during inflation.

Abstract

Magnetohydrodynamic (MHD) waves are analysed in the early Universe, in the inflationary era, assuming the Universe to be filled with a nonviscous fluid of the Zel'dovich type ($p=\rho$) in a metric of the de Sitter form. A spatially uniform, time dependent, magnetic field ${\bf B_0}$ is assumed to be present. The Einstein equations are first solved to give the time dependence of the scale factor, assuming that the matter density, but not the magnetic field, contribute as source terms. The various modes are thereafter analysed; they turn out to be essentially of the same kind as those encountered in conventional nongravitational MHD, although the longitudinal magnetosonic wave is not interpretable as a physical energy-transporting wave as the group velocity becomes superluminal. We determine the phase speed of the various modes; they turn out to be scale factor independent. The Alfv\'{e}n velocity of the transverse magnetohydrodynamic wave becomes extremely small in the inflationary era, showing that the wave is in practice 'frozen in'.