# How to calculate the density of relic neutrinos?

May be not neutrinos, but antineutrinos? Or both types? In the last case, why they didn't annihilate and what is the ratio of relic neutrinos to relic antineutrinos? Is that ratio somehow related to the barion asymmetry?

For reference: Relic neutrinos or cosmic neutrino background

Like the cosmic microwave background radiation (CMB), the cosmic neutrino background is a relic of the big bang

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What are "relic neutrinos"? I'm not familiar with the term, so if you could add a link to some more information, that would be quite helpful. –  David Z Jan 16 '11 at 9:22
@David, I have added the link –  voix Jan 16 '11 at 9:57
Do anti-neutrinos exist? I thought the general belief was that neutrinos were Majorana particles, and so are their own anti-particle. –  Peter Shor Jan 16 '11 at 15:56
"Relic neutrinos" are those that were coupled to the hot early universe (before temperatures dropped below the Z mass) and have since cooled to ridiculously low energies. They have very low cross-sections for interaction with ordinary matter by neutrino physics standards, and such interactions would be lost in the thermal noise anyway. –  dmckee Jan 16 '11 at 18:12
@Peter, R.Davis, 1955. –  voix Jan 16 '11 at 20:12

Even if there's no asymmetry-producing process for neutrinos (like baryogenesis), you still expect a relic neutrino background that's a thermal (Fermi-Dirac) distribution of both neutrinos and antineutrinos, with a temperature of about 2 K. The reason is that, at a certain time in the evolution of the Universe, the density dropped low enough that the neutrino number "froze out": interactions that could change the number of neutrinos (such as primarily $e^- e^+ \leftrightarrow \nu_e\ \bar\nu_e$) became so rare that the time for any given particle to undergo such a reaction grew much longer than a Hubble time.
It's been a long time since I looked at baryogenesis models with any care, but as I recall some models would be expected to produce an asymmetry in the neutrino sector as well. But in practice I don't think that would change the prediction much. The reason is that baryogenesis only has to produce a one part in $10^9$ asymmetry (a billion and one protons for every billion antiprotons). That produces very noticeable effects today, because there was essentially complete annihilation of the antiprotons. But neutrino freeze-out occurs much earlier, while neutrinos are still relativistic, so we don't think that that massive annihilation happened for neutrinos. So even if there is a neutrino-antineutrino asymmetry comparable to the asymmetry produced by baryogenesis, it should only result in a tiny difference in the number of neutrinos over antineutrinos.