Revisiting the quasi-molecular mechanism of recombination

The quasi-molecular mechanism of recombination, recently suggested by Kereselidze et al., is a non-standard process where an electron and two neighboring protons in the early universe directly form an ionized hydrogen molecule in a highly excited state, which then descends to lower levels or dissociates. It has been suggested that the increased binding energy due to the participation of a second proton may lead to an earlier cosmic recombination that alleviates the Hubble tension. Revisiting the quasi-molecular channel of recombination in more details, we find that the original work significantly overestimated the probability of finding a pair of adjacent protons in the relevant epoch ($z\sim$ a few thousand). Our new estimation suggests that the quasi-molecular mechanism of recombination cannot be the primary cause of the Hubble tension.