The latest big splash in physics, the observation of two neutron stars colliding into each other with both gravity waves and light, provides an independent observation of the Hubble constant that when combined with the Planck data tightens the parameter space of neutrino physics.

The sum of the three neutrino masses goes from less than 1.11 eV with Planck data alone, to less than 0.77 eV with this measurement and the Planck data combined. But, without this new data point, but combined with other data sets, the limitation was already even tighter with combinations as low as 0.11 eV, and the minimum value from neutrino oscillation data is 0.06 eV in a normal hierarchy. It isn't clear how much impact this new data point has on the earlier combination value.

The effective number of neutrino types (Neff) goes from 3.11 ± 0.25 with Planck data alone to 3.09 ± 0.25 with the addition of this measurement. But, as of 2015, the constraint with Planck data and other data sets was 3.04 ± 0.18 (even in 2014 cosmology ruled out sterile neutrinos). Neff equal to 3.046 in a case with the three Standard Model neutrinos and neutrinos with masses of 10 eV or more not counting in the calculation. It isn't entirely clear what the Neutron Star measurement of Hubble's constant adds, if anything, to the combined estimates, but it might, for example, slightly reduce the margin of error which would increase the significance by which the four neutrino case was ruled out. Neff and the Hubble constant are strongly correlated, but the combination value for Hubble's constant is very close to the new value from this observation.

So, the four neutrino case is ruled out at a more than 5.3 sigma level already, which is a threshold for a scientific discovery that there are indeed only three neutrinos with masses of 10 eV or less, ruling out the sterile neutrino hypothesis for a stable sterile neutrino of under 10 eV (when a best fit of potential anomalies from reactors predicts a sterile neutrino mass of about 1 eV also here). A 2015 pre-print on notes that:

* The MINOS and MINOS+ reactor experiments rule out a light sterile neutrino, confirming the cosmology result. The abstract of a new pre-print on their results states that:

"A simultaneous fit to the charged-current muon neutrino and neutral-current neutrino energy spectra in the two detectorssin2θ24 for most values of the sterile neutrino mass-splitting Δm241>10−4 eV2 ."

So, the four neutrino case is ruled out at a more than 5.3 sigma level already, which is a threshold for a scientific discovery that there are indeed only three neutrinos with masses of 10 eV or less, ruling out the sterile neutrino hypothesis for a stable sterile neutrino of under 10 eV (when a best fit of potential anomalies from reactors predicts a sterile neutrino mass of about 1 eV also here). A 2015 pre-print on notes that:

The 95% allowed region in parameter space is Neff < 3.7, meff s < 0.52 eV from PlanckTT + lowP + lensing + BAO. This result has important consequences for the sterile neutrino interpretation of short-baseline anomalies. It has been shown that a sterile neutrino with the large mixing angles required to explain reactor anomalies would thermalize rapidly in the early Universe, yielding ∆Neff = 1. The preferred short-baseline solution then corresponds to ms of about 1 eV and ∆Neff = 1 and is strongly excluded (more than 99% confidence) by the above combination of Planck and BAO data.UPDATE October 19, 2017

* The MINOS and MINOS+ reactor experiments rule out a light sterile neutrino, confirming the cosmology result. The abstract of a new pre-print on their results states that:

"A simultaneous fit to the charged-current muon neutrino and neutral-current neutrino energy spectra in the two detectors

**yields no evidence for sterile neutrino mixing using a 3+1 model.**The most stringent limit to date is set on the mixing parameter
The MINOS data explores a range of values for Δm

_{41}between the lightest mass state and the sterile neutrino mass state of 10 meV to 32,000 meV, where the bounds on the sum of the three neutrino masses from cosmology in the currently experimentally preferred normal hierarchy is 60 meV to 110 meV. For example, the MINOS data shows that:At fixed values of ∆m^{2}_{41}the data provide limits on the mixing angles θ_{24}and θ_{34}. At ∆m^{2}_{41}= 0.5 eV^{2}, we find sin^{2}θ_{24}less than [0.0050 (90% C.L.), 0.0069 (95% C.L.)] and sin^{2}θ_{34}less than [0.16 (90% C.L.), 0.21 (95% C.L.)].

* Weak boson decays have long ago ruled out the possibility of a number of weakly interacting neutrinos different than three. The number of weakly interacting neutrinos of less than 45 GeV upon Z boson decay is 2.992 ± 0.007 (with a mean value 1.14 sigma from 3) which is consistent with the Standard Model, in a quantity that must have an integer value. The two neutrino and four neutrino hypotheses are ruled out at the 140+ sigma level, when a mere 5 sigma result is considered scientifically definitive.

END UPDATE

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