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.
