Eur. Phys. J. C (2026) 86: 318
https://doi.org/10.1140/epjc/s10052-026-15600-8

Regular Article - Theoretical Physics

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

Departamento de Física, Universidad Católica del Norte, Avenida Angamos 0610, Antofagasta, Chile

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Received: 3 February 2026
Accepted: 22 March 2026
Published online: 30 March 2026

Abstract

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