Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

Abstract

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 GUT scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields ($\sim 10^{22}$ gauss at $T\sim 100$ GeV with typical inhomogeneity scale $ \sim \frac{ 10^6}{T}$) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through non-linear mechanisms. Previously derived bounds on exotic $B-L$ violating operators may also be evaded.

Revised version, to appear in Phys. Rev. Lett.. Analysis has been extended to larger chemical potentials, for which large magnetic fields survive at the electroweak scale. Previous bounds on $B-L$ violating operators are also evaded in this case