Breakdown of Chiral Perturbation Theory for the Axion Hot Dark Matter Bound.

We show that the commonly adopted hot dark matter bound on the axion mass m_{a}≲1  eV is not reliable, since it is obtained by extrapolating the chiral expansion in a region where the effective field theory breaks down. This is explicitly shown via the calculation of the axion-pion thermalization rate at the next-to-leading order in chiral perturbation theory. We finally advocate a strategy for a sound extraction of the axion hot dark matter bound via lattice QCD techniques.