Axion absorption and the spin temperature of primordial hydrogen

An absorption dip in the spectrum of the cosmic microwave background observed by the EDGES experiment suggests an unexplained reduction of the hydrogen spin temperature at cosmic redshift z ~ 17. The mass of dark-matter axions could correspond to the hyperfine splitting of 5.9 micro-eV, between the triplet (H1) and singlet (H0) state. We calculate the rate for a+ H0 <-> H1 in two ways, and find that it is orders of magnitude smaller than the CMB-mediated transition rate, so irrelevant. As a result, this process cannot be used to rule in or out dark matter axions of mass = hyperfine splitting. The axion rate nonetheless has interesting features, for example, on balance it heats the spin temperature, and the axion couplings to protons and electrons contribute on equal footing.