We compare the quantum chromodynamics (QCD) axion phase-space distribution from unitarized next-to-leading order chiral perturbation theory with the one extracted from pion-scattering data. We derive a robust bound by confronting momentum-dependent Boltzmann equations against up-to-date observations of the cosmic microwave background, of the baryonic acoustic oscillations and of primordial abundances. These datasets imply ma≤0.16 eV for the 95% credible interval, i.e., ∼30% stronger bound than what previously found. We present forecasts using dedicated likelihoods for future cosmological surveys and the sphaleron rate from unquenched lattice QCD. Published by the American Physical Society 2024
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