The QCD Axion: Some Like It Hot

We compare the 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 $m_a\le 0.16$ eV for the 95% credible interval, i.e. $\sim$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.