Future cosmological sensitivity for hot dark matter axions

We study the potential of a future, large-volume photometric survey to constrain the axion mass $m_a$ in the hot dark matter limit. Future surveys such as Euclid will have significantly more constraining power than current observations for hot dark matter. Nonetheless, the lowest accessible axion masses are limited by the fact that axions lighter than $\sim 0.15$ eV decouple before the QCD epoch, assumed here to occur at a temperature $T_{\rm QCD} \sim 170$ MeV; this leaves an axion population of such low density that its late-time cosmological impact is negligible. For larger axion masses, $m_a \gtrsim 0.15$ eV, where axions remain in equilibrium until after the QCD phase transition, we find that a Euclid-like survey combined with Planck CMB data can detect $m_a$ at very high significance. Our conclusions are robust against assumptions about prior knowledge of the neutrino mass. Given that the proposed IAXO solar axion search is sensitive to $m_a\lesssim 0.2$ eV, the axion mass range probed by cosmology is nicely complementary.