Relic Magnetic Fields from Non-Adiabatic Photon Freeze-Out at Recombination

TL;DR

This paper introduces a novel mechanism for generating primordial magnetic fields during recombination through non-adiabatic photon mode squeezing caused by finite relaxation rates.

Contribution

It models the photon-electron plasma as an open system, revealing how relaxation dynamics produce a frozen electromagnetic relic with a specific spectral peak.

Findings

The relic magnetic field spectrum peaks at scales of 10-20 Mpc.

The present-day magnetic field amplitude remains extremely small.

The mechanism explains the origin of a non-equilibrium electromagnetic relic.

Abstract

We propose a new mechanism for generating a primordial electromagnetic relic during the recombination--decoupling transition, based on the rate-dependent thermodynamics of the cosmic photon gas. Treating the photon sector as an open system coupled to the electron plasma, we show that a finite Thomson relaxation rate generates a departure from instantaneous thermal equilibrium, leading to non-adiabatic mode squeezing. As this relaxation rate rapidly decreases across recombination, the system quickly loses the ability to further amplify the deviation, and the squeezing freezes out at a small but finite value. This dynamics is naturally described as a narrow transition layer between an adiabatic tracking regime and a post-relaxation freeze-out regime. By a canonical transformation, the reduced evolution equation is recast into a forced oscillator with a smooth effective potential, clarifying the origin of the squeezing and the selection of the relic scale. Projecting the resulting non-equilibrium electromagnetic relic onto the magnetic sector, we derive the corresponding spectrum and show that its characteristic peak is controlled not by the squeezing parameter alone but by the weighted combination \(k^3\mathscr S_k\). In representative realizations, the peak corresponds today to scales of order \(10\)--\(20\) Mpc, while the present-day field amplitude remains extremely small. The mechanism is therefore better viewed as a source of a frozen non-equilibrium electromagnetic relic than as a complete explanation of the observed cosmic magnetic fields.