Axion-like particles (axions) arise in extensions of the Standard Model and are appealing candidates for the dark matter. In this talk, I discuss some recent work on the bounds derived for the coupling of axions with photons and gluons, using CMB+BAO data. Recent progresses in the field allow to describe the axion-photon and axion-gluon production across various orders of magnitude. For the axion-gluon coupling, I report a stringent bound that is competitive with the results from SN1987A. Axion-photon coupling bounds are competitive for masses above ~3eV. Forecasts on future bounds will also be reported. Based on Caloni et al, JCAP 09 021 (2022), astro-ph/2205.01637
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