  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.
