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 $T\simeq 1$ 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 $R_{\rho }^{(\xi =+1)}(q)={\rho }_q/{\rho }^{\mathrm{std}}$ 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 $N_{\mathrm{eff}}$. The deformation prediction was confronted against CMB$+$BAO and BBN data for $N_{\mathrm{eff}}$ 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 $q_{\mathrm{best}}$.

Comments: 12 pages, 4 figures