New comprehensive description of the scaling evolution of the cosmological magneto-hydrodynamic system

TL;DR

This paper provides an analytical framework for understanding the evolution of primordial magnetic fields in the early universe, considering different physical constraints and dissipation processes, and concludes that magnetogenesis before electroweak symmetry breaking is unlikely.

Contribution

It introduces a comprehensive analytical model combining magnetic helicity and dissipation constraints to describe primordial magnetic field evolution across epochs.

Findings

Magnetic helicity conservation constrains maximally helical fields.

Hosking integral constrains non-helical field evolution.

Magnetogenesis before electroweak symmetry breaking is deemed unfeasible.

Abstract

We study the evolution of primordial magnetic fields until the recombination epoch, which is constrained by the conservation of magnetic helicity density if they are maximally helical and by the Hosking integral if they are non-helical. We combine these constraints with conditions obtained by estimating time scales of energy dissipation processes to describe the evolution of magnetic field strength and magnetic coherence length analytically. The dissipation processes depend on whether magnetic or kinetic energy is dominant, whether the decay dynamics is linear or not, and whether the dominant dissipation term is shear viscosity or drag force. We apply the description to compare constraints on primordial magnetic fields at different epochs in the early universe and argue that magnetogenesis before the electroweak symmetry breaking is not feasible.