Estimate of the primordial magnetic field helicity

TL;DR

It is argued that changes in the non-Abelian Chern-Simons number generate a primordial magnetic field with left-handed helicity, and it is found that the field strength at recombination is approximately 10(-13) G on a comoving coherence scale approximately 0.1 pc.

Abstract

Electroweak baryogenesis proceeds via changes in the non-Abelian Chern-Simons number. It is argued that these changes generate a primordial magnetic field with left-handed helicity. The helicity density of the primordial magnetic field today is then estimated to be given by $\sim 10^2 n_b$ where $n_b\sim 10^{-6}$ /cm$^3$ is the present cosmological baryon number density. With certain assumptions about the inverse cascade we find that the field strength at recombination is $\sim 10^{-13}$ G on a comoving coherence scale $\sim 0.1$ pc.

Figures (1)

• Figure 1: In the first figure, a pair of linked loops of Z-string are shown. They decay by the nucleation of monopole-antimonopole pairs (black circles in the middle figure) which get pulled apart by the strings. Magnetic field ( B) lines (grey curves) run between the monopole and antimonopole. The whole system is embedded in a perfectly conducting plasma in which the B field lines are frozen-in. Finally the strings have decayed, leaving behind a B field configuration with helicity.