The cosmic recombination history in light of EDGES measurements of the cosmic dawn 21-cm signal

The recent EDGES measurements of the global 21-cm signal from the cosmic dawn suggest that the kinetic temperature of the inter-galactic medium (IGM) might be significantly lower compared to its expected value. The colder IGM directly affects the hydrogen recombination of the universe during the cosmic dawn and dark ages by enhancing the rate of recombinations. Here, we study and quantify, the impact of the colder IGM scenario on the recombination history of the universe in the context of DM-baryonic interaction model which is widely used to explain the EDGES 21-cm signal. We find that, in general, the hydrogen ionisation fraction gets suppressed during the dark ages and cosmic dawn and the suppression gradually increases at lower redshifts. However, accurate estimation of the ionisation fraction requires knowledge of the entire thermal history of the IGM, from the thermal decoupling of hydrogen gas and the CMBR to the cosmic dawn. It is possible that two separate scenarios which predict very similar HI differential temperature during the cosmic dawn and are consistent with the EDGES 21-cm signal might have very different IGM temperature during the dark ages. The evolutions of the ionization fraction in these two scenarios are quite different. This prohibits us to accurately calculate the ionisation fraction during the cosmic dawn using the EDGES 21-cm signal alone. We find that the changes in the ionisation fraction w.r.t the standard scenario at redshift $z \sim 17 $ could be anything between $\sim 0 \%$ to $\sim 36 \%$. This uncertainty remains even for a more precise measurement of the 21-cm signal from the cosmic dawn. However, the IGM temperature measured at two widely separated epochs should be able to constrain the ionisation fraction more accurately.