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We reconsider thermal production of axions in the early universe, including axion couplings to all Standard Model (SM>) particles. Concerning the axion coupling to gluons, we find that thermal effects enhance the axion production rate by a factor of few with respect to previous computations performed in the limit of small strong gauge coupling. Furthermore, we find that the top Yukawa coupling induces a much larger axion production rate, unless the axion couples to SM particles only via anomalies.
Salvio et al. (Fri,) studied this question.