  The Peccei-Quinn solution to the strong CP problem provides a motivated
framework rich in cosmological consequence. Thermal axion production is
unavoidable if there is a thermal bath at early times. Scattering and decay
processes of bath particles can dump relativistic axions in the primordial
plasma, and they can leave observable signatures in cosmological observables
probing both the early and the late universe if produced with a significant
abundance. We present recent and significant improvements for the calculation
of the axion production rate for different scenarios and apply these results to
predict the abundance of produced axions. Finally, we provide updated
cosmological bounds on the QCD axion mass.
