PREPRINT

# Speculations on Primordial Magnetic Helicity

John M. Cornwall
arXiv:hep-th/9704022

Submitted on 2 April 1997

## 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 $\sim {l}_{M}{ϵ}^{-1}$, where $ϵ$ 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.

## Preprint

Comment: Latex, 23 pages

Subjects: High Energy Physics - Theory; Astrophysics