Early-Universe Thermal Production of Not-So-Invisible Axions

We find that for Peccei-Quinn symmetry-breaking scales ≲4×${10}^8$ GeV (corresponding to axion masses ≳0.03 eV) thermal production of axions in the early Universe (via the Primakoff and photoproduction processes) dominates coherent production by a factor of about $1200{\left[\frac{m_a}{\left(1\mathrm{} \mathrm{eV}\right)}\right]}^{2.175}$. The photon luminosity from the decays of these relic axions leads to an upper limit to the axion mass of order 2-5 eV. If the axion mass saturates this bound, relic axion decays may well be detectable.