# New cosmological neutrino mass constraint: sum<0.09 eV at 95% CL

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TL;DR Summary
Updated cosmological neutrino mass constraints start disfavoring the inverted mass ordering
arXiv: On the most constraining cosmological neutrino mass bounds

From neutrino mixing we know that an inverted order (two "heavy" neutrinos, one light neutrino) needs a sum of masses of at least ~0.09 eV, while the normal order (two light, one "heavy") can have a sum as low as ~0.05 eV. The measurement is not sensitive enough to clearly rule out the inverted order, but it's a contribution to the question. Other experiments tend to favor the normal order, too. As the name suggests it's the one we expect anyway, because it follows the pattern we see elsewhere.
The best fit seems to be a sum of zero, or even negative values if they would be allowed, but the physical region is within the uncertainties.

Their fit also produces a Hubble constant of 68.00 +- 0.88 km/(s\*Mpc), close to the Planck results - probably not surprising as they largely use the same data.

vanhees71 and fresh_42

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As the name suggests it's the one we expect anyway, because it follows the pattern we see elsewhere.
Well, yes and no. It is indeed what we observe in other fermions (ie, quarks and charged leptons). However, we also know that the neutrino sector is quite different from the other sectors, including in terms of the mass generation mechanism. However, with reasonable assumptions on the mass generation mechanism, it is typically easier to end up with a normal ordering scenario anyway mainly due to the fine tuning of the heavier state masses that would be required to produce an inverted ordering scenario.

vanhees71
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Well, yes and no. It is indeed what we observe in other fermions (ie, quarks and charged leptons).

and let's remember that, mass ordered, the quark generations are (+2/3, -1/3) (-1/3, +2/3), (-1/3, +2/3) so something peculiar happens with the weak isospin: it is inverted in first generation, and huge in third generation. So, it would not be surprising if family number also has peculiarities, mass-wise

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Fleshing out what the paper says a little more specifically, the paper fixes the bound of the sum of the three neutrino masses from cosmology data as set for in the body text is to 87 meV/c^2 or less with 95% confidence, using a novel way of combining multiple sources of data.

This would seem to rule out the inverted neutrino mass hierarchy (for which the sum of the three neutrino masses exceeds 100 meV). It also reduces the uncertainties in the absolute neutrino masses, which have a minimum value (determined from mass differences in neutrino oscillations and assuming a lightest neutrino mass of almost zero) of about 60 meV. Thus, most uncertainty in the sum of the neutrino masses is the shared 0-9 meV range of uncertainty in the lightest neutrino mass.

The best fit point of the data (i.e. within the one sigma range), constrained by the minimum sum of the three neutrino masses from neutrino oscillation data, is very close to the minimum non-zero value that implies a lightest neutrino mass that is on the order of 1 meV or less.

Without the neutrino oscillation data constraint, the best fit point from cosmology data is actually slightly below the minimum sum of neutrino masses from neutrino oscillation data, although the preference for the below 60 meV value is not statistically significant.

The paper and its abstract are as follows:

We present here up-to-date neutrino mass limits exploiting the most recent cosmological data sets. By making use of the Cosmic Microwave Background temperature fluctuation and polarization measurements, Supernovae Ia luminosity distances, Baryon Acoustic Oscillation observations and determinations of the growth rate parameter, we are able to set the most constraining bound to date, ∑mν<0.09~eV at 95%~CL. This very tight limit is obtained without the assumption of any prior on the value of the Hubble constant and highly compromises the viability of the inverted mass ordering as the underlying neutrino mass pattern in nature. The results obtained here further strengthen the case for very large multitracer spectroscopic surveys as unique laboratories for cosmological relics, such as neutrinos: that would be the case of the Dark Energy Spectroscopic Instrument (DESI) survey and of the Euclid mission.
Eleonora Di Valentino, Stefano Gariazzo, Olga Mena "On the most constraining cosmological neutrino mass bounds" arXiv:2106.16267 (June 29, 2021).

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and let's remember that, mass ordered, the quark generations are (+2/3, -1/3) (-1/3, +2/3), (-1/3, +2/3) so something peculiar happens with the weak isospin: it is inverted in first generation, and huge in third generation. So, it would not be surprising if family number also has peculiarities, mass-wise
Why would you order all 6 quarks by mass? They are two different groups.
u << c << t
d << s << b (neglecting mixing)
e << mu << tau

nu_1 << nu_2 << nu_3 looks more natural than nu_3 << nu_1 ##\approx## nu_2, independent of the mass source

ohwilleke