Impact of Helical Electromagnetic Fields on the Axion Window
  Primordial electromagnetic fields can strongly affect the cosmic evolution of
axions, and vice versa. We show that if helical electromagnetic fields are
coherently produced in the early universe, their remnants source a field
velocity to the coupled axions and enhance the relic abundance of axion dark
matter. We discuss the implications for the QCD axion and axion-like particles
that are coupled to the SM or hidden gauge groups. For a QCD axion coupled to
hidden photons, we find that the conventional window for the axion decay
constant $10^{8}\, \mathrm{GeV} \lesssim f \lesssim 10^{12}\, \mathrm{GeV}$ can
be completely closed due to overproduction of axion dark matter by helical
electromagnetic fields as little as $\alpha \, \Delta N_{\mathrm{eff}} \gtrsim
10^{-12}$, where $\alpha$ is the gauge coupling and $\Delta N_{\mathrm{eff}}$
is the effective extra relativistic degrees of freedom of the hidden photons.
