Estimate of the Primordial Magnetic Field Helicity

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 $n_b\sim {10}^{-6\mathrm{}}/{\mathrm{cm}}^3$ is the present cosmological baryon number density. With certain assumptions about the inverse cascade we find that the field strength at recombination is $\sim {10}^{-13\mathrm{}}\mathrm{G}$ on a comoving coherence scale $\sim 0.1\mathrm{pc}$.