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 _ { 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 .