Cosmological bound on the QCD axion mass, redux

We revisit the joint constraints in the mixed hot dark matter scenario in which both thermally produced QCD axions and relic neutrinos are present. Upon recomputing the cosmological axion abundance via recent advances in the literature, we improve the state-of-the-art analyses and provide updated bounds on axion and neutrino masses. By avoiding approximate methods, such as the instantaneous decoupling approximation, and limitations due to the limited validity of the perturbative approach in QCD that forced to artificially divide the constraints from the axion-pion and the axion-gluon production channels, we find robust and self-consistent limits. We investigate the two most popular axion frameworks: KSVZ and DFSZ. From Big Bang Nucleosynthesis (BBN) light element abundances data we find for the KSVZ axion ΔN eff < 0.31 and an axion mass bound ma < 0.53 eV (i.e., a bound on the axion decay constant fa > 1.07 × 107 GeV) both at 95% CL. These BBN bounds are improved to Δ N eff < 0.14 and ...