# Are there any experimental bounds on the ratio of neutrinos to antineutrinos in the universe?

In the Standard Model, both baryon number and lepton number are conserved quantities (excluding the theoretical possibility of sphaleron processes which are exceeding rare, at least at non-"near in time to the Big Bang" energies of circa 10 TeV or more). We have a good estimate of the total baryon number of the universe. But, we don't have nearly so good an estimate of the total lepton number of the universe (and in many beyond the Standard Model theories, $B$ and $L$ are not conserved but either $B-L$ or $B+L$ are conserved).

The number of baryons in the universe is about $4\times10^{79}$, and the number of neutrinos in the universe is about $1.2\times10^{89}$.

We know that the ratio of baryon antimatter to baryon matter (and the ratio of charged antileptons to charged leptons) is on the order of $10^{-11}$.

And, we know that to considerable precision there are 2 neutrons for every 14 protons in the universe (this is a confirmed prediction of Big Bang Nucleosynthesis), and that the number of charged leptons is almost identical to the number of protons in the universe.

The number of mesons and baryons other than neutrons and protons is negligible at any given time in nature since they are so short lived and generated only at high energies. (Also, the baryon number of a meson is zero.)

But, the total lepton number of the universe (and the total value of $B-L$ and $B+L$ for the universe), is dependent almost entirely upon the ratio of antineutrinos to neutrinos in the universe, since there are about a billion times as many neutrinos as there are charged leptons (or baryons) in the universe.

Incidentally, the ratio would still be the principle determinant of the total lepton number of the universe even if dark matter particles had a lepton number if the dark matter particles has masses in the keV mass range or above.

I am aware of one paper from 2013 that finds suggestive evidence that there are more antineutrinos than neutrinos in the universe without really quantifying that ratio or putting margins of error on it, but I am wondering, are there any better experimental bounds on the ratio of neutrinos to antineutrinos in the universe?

Another 2002 paper puts an upper bound on electron neutrino asymmetry at 3% of the number of electron neutrinos, and a bound on muon and tau neutrino asymmetry at 50% of the combined number of such neutrinos, but I'm not clear that this reflects current research or that its methods are sound. The 2002 paper and another 2009 paper seem to see Big Bang Nucleosynthesis as a limit on this ratio, although I don't really quite follow the reasoning of these papers.

• This may be relevant: physics.stackexchange.com/questions/254357/… – Ihle Jan 31 '17 at 1:41
• arxiv.org/abs/1211.6721 – ohwilleke Jul 6 '18 at 15:25
• "The largest allowed (2σ) neutrino chemical potential |ξf | = 0.45 leads to ∆Neff = 0.266, fully consistent with CMB observations. [Ed. the constraint on delta Neff is now less than .008]. The helium fraction reported by CMB observations results in a negative neutrino chemical potential ξf ∼ −0.2 and ∆Neff ∼ 0.1. In that case we would live in a Universe ruled by anti-neutrinos." – ohwilleke Jul 6 '18 at 15:36