Resolving the H_0 and S_8 tensions with neutrino mass and chemical potential

A simple and natural extension of the standard ΛCDM model is to allow relic neutrinos to have non-zero degeneracy. We confront this ΛCDMξ model, ΛCDM with neutrino mass M_ν and degeneracy ξ_3 as additional parameters, with the Planck TT, lowT, plik–lensing, BAO, and DES datasets, and we observe a strong preference (Bayes factor log_10B=1.9) for it over the standard ΛCDM model. Both the H_0 and S_8 tensions are resolved to within 1σ with the same set of neutrino parameters, along with 3σ evidence for nonzero neutrino mass (M_ν=0.58^+0.17_-0.13 eV) and degeneracy (ξ_3=1.27^+0.42_-0.22). Furthermore, our analysis favors the scalar index n_s to be slightly larger than 1, compatible with some hybrid inflation models, as well as a significantly larger optical depth τ than the standard Planck value, indicating an earlier onset of reionization.