Axions can play very important roles in cosmology. They are interesting candidates for dark matter, dark energy, inflation but also, in the case of the QCD axion, a natural solution to the strong CP problem.
Interestingly, because of their small masses, the couplings to SM particles are rather weakly constrained but cosmological and astrophysical observables can provide significant help in probing such couplings.
In this talk I will discuss one of such observables, the number of effective degrees of freedom (Neff) measured in the CMB, which will be measured with greater precision in the near future. I will show how the axion can thermalize with the primordial plasma at temperatures below and above the QCD-PT through the couplings with SM fermions and leave a sizeable effect on Neff. In particular, if the coupling is with SM leptons such effect can, in some cases, decrease the current tension on the observed value of the Hubble parameter between different experiments.