Resolving the H₀ and S₈ 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 ξ₃ as additional parameters, with the Planck TT, lowT, plik--lensing, BAO, and DES datasets, and we observe a strong preference (Bayes factor log₁₀B=1.9) for it over the standard ΛCDM model. Both the H₀ and S₈ 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 (ξ₃=1.27+0.42-0.22). Furthermore, our analysis favors the scalar index nₛ 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.