Speculations on Primordial Magnetic Helicity

TL;DR

This paper explores the hypothesis that primordial magnetic fields generated around the electroweak phase transition possess significant helicity linked to baryon and lepton numbers, with potential implications for cosmic structure and magnetic field evolution.

Contribution

It proposes a mechanism for primordial magnetic helicity generation connected to B+L violation and analyzes its evolution and effects through a quasi-linear general-relativistic MHD framework.

Findings

Magnetic helicity could be conserved from early universe to matter decoupling.

Helicity-driven inverse cascade can amplify magnetic field scales.

Generated magnetic fields may influence early structure formation and CP violation signatures.

Abstract

We speculate that above or just below the electroweak phase transition magnetic fields are generated which have a net helicity (otherwise said, a Chern-Simons term) of order of magnitude $N_B + N_L$, where $N_{B,L}$ is the baryon or lepton number today. (To be more precise requires much more knowledge of B,L-generating mechanisms than we currently have.) Electromagnetic helicity generation is associated (indirectly) with the generation of electroweak Chern-Simons number through B+L anomalies. This helicity, which in the early universe is some 30 orders of magnitude greater than what would be expected from fluctuations alone in the absence of B+L violation, should be reasonably well-conserved through the evolution of the universe to around the times of matter dominance and decoupling, because the early universe is an excellent conductor. Possible consequences include early structure formation; macroscopic manifestations of CP violation in the cosmic magnetic field (measurable at least in principle, if not in practice); and an inverse-cascade dynamo mechanism in which magnetic fields and helicity are unstable to transfer to larger and larger spatial scales. We give a quasi-linear treatment of the general-relativistic MHD inverse cascade instability, finding substantial growth for helicity of the assumed magnitude out to scales $\sim l_M\epsilon^{-1}$, where $\epsilon$ is roughly the B+L to photon ratio and $l_M$ is the magnetic correlation length. We also elaborate further on an earlier proposal of the author for generation of magnetic fields above the EW phase transition.