Bounds on the Tsallis parameter from a deformed neutrino sector in the early Universe

We generalize neutrino energy density content in the early Universe near BBN era T 1 T ≃ 1 MeV within Tsallis nonextensive statistics. By using Curado–Tsallis constraints we obtain generalized distribution functions fq(E) f q ( E ) . We compute the generalized thermodynamic integral for the energy density ρ q ρ q . We define a reescaling which is a ratio between the deformed energy density and the standard extensive case. The last was used to directly map and deform neutrino content via the effective number of neutrinos Nₑff N eff . The deformation prediction was confronted against CMB+BAO and BBN data for Nₑff N eff by a joint/combined χ ² χ 2 type-fit. We obtained the constraints |q-1|≤ 1.09× 10⁻² | q - 1 | ≤ 1.09 × 10 - 2 (95% CL) and |q-1|≤ 1.32× 10⁻² | q - 1 | ≤ 1.32 × 10 - 2 (99% CL) from the combined analysis by numerically calculating the best value of the Tsallis parameter qbest q best .