Early cosmological evolution of primordial electromagnetic fields

It is usually assumed that when Weyl invariance is unbroken in the electromagnetic sector, the energy density of primordial magnetic fields will redshift as radiation. Here we show that primordial magnetic fields do not exhibit radiation-like redshifting in the presence of stronger electric fields, as a consequence of Faraday's law of induction. In particular for the standard Maxwell theory, magnetic fields on super-horizon scales can redshift as $B^2 \propto a^{-6} H^{-2}$, instead of the usually assumed $a^{-4}$. Taking into account this effect for inflationary magnetogenesis can correct previous estimates of the magnetic field strength by up to 37 orders of magnitude. This opens new possibilities for inflationary magnetogenesis, and as an example we propose a scenario where femto-Gauss intergalactic magnetic fields are created on Mpc scales, with high-scale inflation producing observable primordial gravitational waves, and reheating happening at low temperatures.