Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

In the standard model there are charges with Abelian anomaly only (e.g., right-handed electron number) which are effectively conserved in the early Universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the grand unified theory scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields ( ~10²² G at T~100 GeV with typical inhomogeneity scale ~10⁶T) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through nonlinear mechanisms. Previously derived bounds on exotic B-L violating operators may also be evaded.