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

TL;DR

This paper introduces a new analytical framework for understanding the evolution of primordial magnetic fields in the early universe, highlighting slow decay and inverse transfer phenomena due to Hosking integral conservation.

Contribution

It provides a novel classification of magnetic field decay regimes and analytic models that interpret numerical simulations, challenging conventional views on magnetic field decay.

Findings

Magnetic field decay is generally slow due to Hosking integral conservation.

The evolution can be categorized into four regimes based on decay dynamics and dissipation mechanisms.

Inverse transfer of magnetic energy is a common feature in the evolution of primordial magnetic fields.

Abstract

We present a new description of cosmological evolution of the primordial magnetic field under the condition that it is non-helical and its energy density is larger than the kinetic energy density. We argue that the evolution can be described by four different regimes, according to whether the decay dynamics is linear or not, and whether the dominant dissipation term is the shear viscosity or the drag force. Using this classification and conservation of the Hosking integral, we present analytic models to adequately interpret the results of various numerical simulations of field evolution with variety of initial conditions. It is found that, contrary to the conventional wisdom, the decay of the field is generally slow, exhibiting the inverse transfer, because of the conservation of the Hosking integral. Using the description proposed here, we may trace the intermediate evolution history of the magnetic field and clarify whether each process governing its evolution is frozen or not, which is essential to follow the evolution of relatively weak magnetic fields.