Cosmological magnetic fields from primordial helicity

Primordial magnetic fields may account for all or part of the fields observed in galaxies. We consider the evolution of the magnetic fields created by pseudoscalar effects in the early universe. Such processes can create force-free fields of maximal helicity; we show that, for such a field, magnetic energy inverse cascades to larger scales than it would have solely by flux freezing and cosmic expansion. For fields generated at the electroweak phase transition, we find that the predicted wavelength today can in principle be as large as $\sim 10\hspace{0.5em}\mathrm{kpc},$ and the field strength can be as large as $\sim {10}^{-10}\hspace{0.5em}\mathrm{G}.$