Abstract A simple and natural extension of the standard Lambda cold dark matter (ΛCDM) model is to allow relic neutrinos to have finite chemical potentials. We confront this ΛCDM ξ model, a ΛCDM with neutrino mass M ν and degeneracy ξ 3 as additional parameters, with various cosmological data sets. We find that the H 0 and S 8 tensions become significant only in the presence of the cosmic microwave background (CMB) polarization data. Specifically, the global and local measurements agree to within 0.8 σ and 1.6 σ for the H 0 and S 8 tensions, respectively, when the CMB polarization data are not included. Therefore, the H 0 and S 8 tensions exist between CMB temperature and polarization data, both being global measurements. Fitting the ΛCDM ξ model to the CMB temperature data, we find 3 σ evidence for nonzero neutrino mass ( M ν = 0.5 7 − 0.13 + 0.17 eV ) and degeneracy ( ξ 3 = 1.1 3 − 0.19 + 0.41 ), and the O ( 1 ) neutrino degeneracy parameter is compatible with Big Bang nucleosynthesis data. The scalar index n s exceeds 1 slightly, which is compatible with some hybrid inflation models. Furthermore, the recent DESI baryon acoustic oscillation data prefer the ΛCDM ξ model to the Planck ΛCDM model. Similar results are obtained when including additional supernova data, while the inclusion of the Atacama Cosmology Telescope τ prior shifts the preferred M ν and ξ 3 values closer to zero and brings n s back to the values favored when the polarization data are included.
Yeung et al. (Tue,) studied this question.