Constraining Tsallis Corrections to Photon Reheating from Electron-Positron Annihilation

In this work we generalize the entropy transfer from electron-positron annihilation to photons in the early Universe. The generalization is implemented within the Tsallis formalism by using generalized distribution functions derived from Curado-Tsallis constraints. Through this deformation, the entropy density of the electromagnetic sector is modified, while the photon component is kept extensive. Therefore, the nonextensive correction is introduced only in the $e^-e^+$ pairs. This affects the entropic degrees of freedom before electron-positron annihilation and consequently modifies the temperature ratio $T_\nu/T_\gamma$. The resulting correction is then mapped into the effective number of relativistic species, $N_{\rm eff}$. Finally, by performing a combined $\chi^2$ analysis using CMB$+$BAO and BBN data, we obtain the $2\sigma$ bound $|q-1|\leq 1.3\times10^{-2}$ for the nonextensive parameter. This result implies that any departure or correction from Boltzmann-Gibbs extensivity must remain small during the MeV era.