Hydrogen spin oscillations in a background of axions and the 21-cm brightness temperature

The 21-cm line signal arising from the hyperfine interaction in hydrogen has an important role in cosmology and provides a unique method for probing of the universe prior to the star formation era. We propose that the spin flip of Hydrogen by the coherent emission/absorption of axions causes a lowering of their spin temperature and can explain the stronger than expected absorption of 21-cm light reported by the EDGES collaboration. We find the analogy of axion interaction with the two-level HI with the Jaynes-Cummings model of a two-level atom in a cavity and we derive the spin-flip frequency in this formalism and show that the coherent oscillations frequency Omega proportional to 1/f(a) in contrast with the incoherent transitions between the HI hyperfine levels where the transition rates proportional to 1/f(a)(2). The axion emission and absorption rates are equal but the spin temperature is still lowered due to different selection rules for the spin-flip transitions compared to the photon process. We show that the axion process goes in the right direction for explaining the EDGES observation. For this mechanism to work, we require a coherent field of relativistic axions with energy E-v peaked at the 21-cm spin-flip energy. Such a coherent background of relativistic axions can arise from the decay of cosmic strings if the decay takes place in the electroweak era.