Comment on "21-cm Radiation: A New Probe of Variation in the Fine-Structure Constant"

Khatri and Wandelt reported that change in the value of alpha by 1% changes the mean brightness temperature $T_b$ decrement of the CMB due to 21 cm absorption by 5% over the redshift range z $<$ 50. A drawback of their approach is that the dimensionful parameters are used. Changing of units leads to the change of the magnitude and even sign of the effect. Similar problems may be identified in a large number of other publications which consider limits on the variation of alpha using dimentionful parameters. We propose a method to obtain consistent results and provide an estimate of the effect.