Reionization during the dark ages from a cosmic axion background

Recently it has been pointed out that a cosmic background of relativistic axion-like particles (ALPs) would be produced by the primordial decays of heavy fields in the post-inflation epoch, contributing to the extra-radiation content in the Universe today. Primordial magnetic fields would trigger conversions of these ALPs into sub-MeV photons during the dark ages. This photon flux would produce an early reionization of the Universe, leaving a significant imprint on the total optical depth to recombination $\tau$. Using the current measurement of $\tau$ and the limit on the extra-radiation content $\Delta N_{\rm eff}$ by the Planck experiment we put a strong bound on the ALP-photon conversions. Namely we obtain upper limits on the product of the photon-ALP coupling constant $g_{a\gamma}$ times the magnetic field strength $B$ down to $g_{a\gamma} B \gtrsim 6 \times 10^{-18} \textrm{GeV}^{-1} \textrm{nG}$ for ultralight ALPs.