Thermal Axions: What’s Next?

Scatterings and decays of thermal bath particles in the early universe can release new relativistic degrees of freedom into the primordial plasma. We focus on the QCD axion, emphasizing recent advancements in the predictions of its contribution to cosmological observables. We provide a comprehensive review of the state-of-the-art calculations for the axion production rate across different energy scales during the cosmic expansion and outline the key developments required for future progress in this area. Subsequently, we present a phase-space approach to refine predictions for the axion dark radiation abundance. This methodology allows for the examination of light particles that never reach thermal equilibrium throughout the evolution of the universe, facilitating a detailed analysis of their decoupling processes. We show how spectral distortions arise from non-instantaneous decoupling and quantify their observable effects.