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

Abstract We generalize neutrino energy density content in the early Universe near BBN era $$T\simeq 1$$ T ≃ 1 MeV within Tsallis nonextensive statistics. By using Curado–Tsallis constraints we obtain generalized distribution functions $$f_q(E)$$ f q ( E ) . We compute the generalized thermodynamic integral for the energy density $$\rho _q$$ 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 $$N_\textrm{eff}$$ N eff . The deformation prediction was confronted against CMB+BAO and BBN data for $$N_\textrm{eff}$$ N eff by a joint/combined $$\chi ^2$$ χ 2 type-fit. We obtained the constraints $$|q-1|\le 1.09\times 10^{-2}$$ | q - 1 | ≤ 1.09 × 10 - 2 (95% CL) and $$|q-1|\le 1.32\times 10^{-2}$$ | q - 1 | ≤ 1.32 × 10 - 2 (99% CL) from the combined analysis by numerically calculating the best value of the Tsallis parameter $$q_\textrm{best}$$ q best .