Cosmological production of H_2 before the formation of the first   galaxies
  Previous calculations of the pregalactic chemistry have found that a small amount of H_2, x[H_2]=n[H_2]/n[H] = 2.6e-6, is produced catalytically through the H^-, H_2^+, and HeH^+ mechanisms. We revisit this standard calculation taking into account the effects of the nonthermal radiation background produced by cosmic hydrogen recombination, which is particularly effective at destroying H^- via photodetachment. We also take into consideration the non-equilibrium level populations of H_2^+, which occur since transitions among the rotational-vibrational levels are slow compared to photodissociation. The new calculation predicts a final H_2 abundance of x[H_2] = 6e-7 for the standard cosmology. This production is due almost entirely to the H^- mechanism, with ~1 per cent coming from HeH^+ and ~0.004 per cent from H_2^+. We evaluate the heating of the diffuse pregalactic gas from the chemical reactions that produce H_2 and from rotational transitions in H_2, and find them to be negligible. 
Christopher M. Hirata, Nikhil Padmanabhan