Origin of primordial magnetic fields

Abstract

Magnetic fields of intensities similar to those in our galaxy are also observed in high redshift galaxies, where a mean field dynamo would not have had time to produce them. Therefore, a primordial origin is indicated. It has been suggested that magnetic fields were created at various primordial eras: during inflation, the electroweak phase transition, the quark-hadron phase transition (QHPT), during the formation of the first objects, and during reionization. We suggest here that the large-scale fields $\ensuremath{\sim}\ensuremath{\mu}\mathrm{G}$, observed in galaxies at both high and low redshifts by Faraday rotation measurements (FRMs), have their origin in the electromagnetic fluctuations that naturally occurred in the dense hot plasma that existed just after the QHPT. We evolve the predicted fields to the present time. The size of the region containing a coherent magnetic field increased due to the fusion of smaller regions. Magnetic fields (MFs) $\ensuremath{\sim}10\text{ }\text{ }\ensuremath{\mu}\mathrm{G}$ over a comoving $\ensuremath{\sim}1\text{ }\text{ }\mathrm{pc}$ region are predicted at redshift $z\ensuremath{\sim}10$. These fields are orders of magnitude greater than those predicted in previous scenarios for creating primordial magnetic fields. Line-of-sight average MFs $\ensuremath{\sim}{10}^{\ensuremath{-}2}\text{ }\text{ }\ensuremath{\mu}\mathrm{G}$, valid for FRMs, are obtained over a 1 Mpc comoving region at the redshift $z\ensuremath{\sim}10$. In the collapse to a galaxy (comoving size $\ensuremath{\sim}30\text{ }\text{ }\mathrm{kpc}$) at $z\ensuremath{\sim}10$, the fields are amplified to $\ensuremath{\sim}10\text{ }\text{ }\ensuremath{\mu}\mathrm{G}$. This indicates that the MFs created immediately after the QHPT (${10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{s}$), predicted by the fluctuation-dissipation theorem, could be the origin of the $\ensuremath{\sim}\ensuremath{\mu}\mathrm{G}$ fields observed by FRMs in galaxies at both high and low redshifts. Our predicted MFs are shown to be consistent with present observations. We discuss the possibility that the predicted MFs could cause non-negligible deflections of ultrahigh energy cosmic rays and help create the observed isotropic distribution of their incoming directions. We also discuss the importance of the volume average magnetic field predicted by our model in producing the first stars and in reionizing the Universe.