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The advent of precise measurements of the cosmic microwave background (CMB) anisotropies has motivated correspondingly precise calculations of the cosmic recombination history. Cosmic recombination proceeds far out of equilibrium because of a bottleneck at the $n=2$ level of hydrogen: atoms can only reach the ground state via slow processes: two-photon decay or Lyman-$alpha$ resonance escape. However, even a small primordial abundance of molecules could have a large effect on the interline opacity in the recombination epoch and lead to an additional route for hydrogen recombination. Therefore, this paper computes the abundance of the H$_2$ molecule during the cosmic recombination epoch. Hydrogen molecules in the ground electronic levels X$^1Sigma^+_g$ can either form from the excited H$_2$ electronic levels B$^1Sigma^+_u$ and C$^1Pi_u$ or through the charged particles H$_2^+$, HeH$^+$ and H$^-$. We follow the transitions among all of these species, resolving the rotational and vibrational sub-levels. Since the energies of the X$^1Sigma^+_g$--B$^1Sigma^+_u$ (Lyman band) and X$^1Sigma^+_g$-C$^1Pi_u$ (Werner band) transitions are near the Lyman-$alpha$ energy, the distortion of the CMB spectrum caused by escaped H Lyman-line photons accelerates both the formation and the destruction of H$_2$ due to this channel relative to the thermal rates. This causes the populations of H$_2$ molecules in X$^1Sigma^+_g$ energy levels to deviate from their thermal equilibrium abundances. We find that the resulting H$_2$ abundance is $10^{-17}$ at $z=1200$ and $10^{-13}$ at $z=800$, which is too small to have any significant influence on the recombination history.
We compute the spectral distortions of the Cosmic Microwave Background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1 GHz-3500 GHz. We follow t
We discuss the evolution of the ratio in number of recombinations due to 2s two photon escape and due to the escape of Lyman-$alpha$ photons from the resonance during the epoch of cosmological recombination, within the width of the last scattering su
Characterizing the epoch of reionization (EoR) at $zgtrsim 6$ via the redshifted 21 cm line of neutral Hydrogen (HI) is critical to modern astrophysics and cosmology, and thus a key science goal of many current and planned low-frequency radio telesco
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