Inverted Neutrino Hierarchy Disfavored By DESI

The DESI collaboration has found that the sum of the three neutrino masses should be less than 0.071 eV at 95% confidence (assuming as a prior only that the sum of the neutrino masses is greater than zero). This disfavors an inverted neutrino hierarchy the demands roughly a minimum of a 0.100 eV sum of neutrino masses, while a normal neutrino hierarchy requires a minimum sum of neutrino masses of only about 0.059 eV. The preference for a normal hierarchy is only about two sigma, however. This estimate is heavily dependent upon the assumed dark energy model, however, and assumes a fixed cosmological constant. 

The upper bound on the sum of the neutrino masses from direct measurements at KATRIN is about 1.35 eV, a cap that is likely to fall by about 0.75 eV to 0.60 eV when the KATRIN experiment is concluded. The upper limit based upon cosmology observations, as of 2020, was about 0.130 eV, and DESI significantly tightens this bound. Of course, direct measurement bounds on the absolute neutrino masses remain much weaker than those from cosmology, and will continue to be weaker for the foreseeable future.

The number of effective neutrino species N(eff) is estimated by DESI to be 3.18 ± 0.16 compared to the expected value of 3.044 if the only neutrinos are the three Standard Model active neutrinos, a possibility that is compatible at the one sigma level. This disfavors a model with four or more neutrinos impacting N(eff) at more than the five sigma level (as well as disfavoring the already ruled out possibility that there are two or fewer neutrino flavors at more than five sigma), consistent with past cosmological estimates of N(eff). This is a slightly higher value of N(eff) than a prior DESI analysis, due to this paper's additional consideration of "full shape" information, but the difference is immaterial given that the number of neutrino flavors is a quantity that changes in integer increments.

The loophole in the N(eff) measurement, however, is that a very massive fourth neutrino species would not register as a neutrino contributing to the number of effective neutrino species.

For example, a 50 GeV mass fourth generation active neutrino would not change N(eff).

In addition to its conclusions about neutrinos, the DESI collaboration concludes that the late time Hubble constant value is 68.40 ± 0.27 in  the usual units, which is closer to the CMB based determination of it of 67.66 ± 0.42, which is consistent with the new DESI estimate at the 1.5 sigma level, than many other efforts to determine the late time Hubble constant have suggested. The DESI results still prefer a non-constant amount of dark energy, however.