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Energy exchange processes play a crucial role in the early Universe,affecting the thermal balance and the dynamical evolution of the primordialgas. In the present work we focus on the consequences of a non-thermaldistribution of the level populations of H$_2$: first, we determine theexcitation temperatures of vibrational transitions and the non-equilibrium heattransfer; second, we compare the modifications to chemical reaction ratecoefficients with respect to the values obtained assuming local thermodynamicequilibrium; third, we compute the spectral distortions to the cosmicbackground radiation generated by the formation of H$_2$ in vibrationallyexcited levels. We conclude that non-equilibrium processes cannot be ignored incosmological simulations of the evolution of baryons, although theirobservational signatures remain below current limits of detection. New fits tothe equilibrium and non-equilibrium heat transfer functions are provided.

Non-equilibrium H$_2$ formation in the early Universe: energy exchanges, rate coefficients and spectral distortions