A new calculation of the predicted value of the observable N(eff) (for the effective number of neutrinos) from cosmology data when there are exactly three neutrino flavors predicts that N(eff) = 3.0439 ± 0.0006.
The commonly quoted value determined with a somewhat less precise model is 3.045 which is consistent with the new value at the two sigma level.
Astronomy observations are consistent with these predicted values. We know that there are at least three neutrino flavors, but astronomy observations rule out the possibility of four or more neutrino flavors at high significance. This measure of the number of neutrino flavors would include sterile neutrinos that oscillate with the three ordinary active neutrinos up to about 1-10 eV of mass (which is far more massive than any of the active neutrino masses). But a sterile neutrino that is much more massive than that would not impact the value of the N(eff) observable.
W and Z boson decays rule out a fourth generation active neutrino up to masses of about 45.6 GeV.
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