Reynolds numbers in the early Universe

TL;DR

The paper investigates the magnetic Reynolds number in the early Universe, revealing it was vastly larger than the kinetic Reynolds number, and explores implications for magnetic field evolution and diffusion scales before electron-positron annihilation.

Contribution

It introduces a novel analysis of magnetic Reynolds numbers in the early Universe, linking them to curvature perturbations and entropy during plasma evolution.

Findings

Magnetic Reynolds number was about twenty orders of magnitude larger than the kinetic one.

Large-scale inhomogeneities are driven by scalar curvature fluctuations.

Reynolds numbers prior to electron-positron annihilation relate to the entropy in the Hubble volume.

Abstract

After electron-positron annihilation and prior to photon decoupling the magnetic Reynolds number is approximately twenty orders of magnitude larger than its kinetic counterpart which is, in turn, smaller than one. In this globally neutral system the large-scale inhomogeneities are provided by the spatial fluctuations of the scalar curvature. Owing to the analogy with the description of Markovian conducting fluids in the presence of acoustic fluctuations, the evolution equations of a putative magnetic field are averaged over the large-scale flow determined by curvature perturbations. General lessons are drawn on the typical diffusion scale of magnetic inhomogeneities. It is speculated that Reynolds numbers prior to electron-positron annihilation can be related to the entropy contained in the Hubble volume during the various stages of the evolution of the conducting plasma.