Effects of pair freeze-out on photon distributions in BBN epoch

We investigate the evolution of non-extensivity in the photon distribution during the Big Bang Nucleosynthesis (BBN) epoch using Tsallis statistics. Assuming a minimal deviation from the Planck distribution, we construct the perturbed Boltzmann equation for photons, including the collision terms for pair creation and annihilation processes. We analyze the possibility that these collisions could cause a slight increase in the number of high-frequency photons within the BBN era, and consequently, the primordial plasma might be temporarily placed in a state of chemical non-equilibrium. We also discuss the restoration of the photon distribution to an equilibrium state as the Universe enters the matter-dominated era. These findings, which suggest possible changes in the photon distribution during the epoch between the BBN and the recombination, offer insights that support the previously proposed ansatz solution to the primordial lithium problem in arXiv:1812.09472.