# Are ultra-cold neutrinos an option for cold dark matter? [duplicate]

Nobody hass seen cold dark matter. Are ultra-cold (non-relativistic) neutrinos, below 1 fK (femtokelvin), an option for dark matter?

This is a question about normal neutrinos - electron neutrinos and muon neutrinos and tau neutrinos - and not any additional, invented neutrino types.

This is a question about neutrinos that are not in the cosmic neutrino background, which have a temperature of 1.95K.

The question is about cosmological dark matter, not about galactic dark matter.

Their density could be large enough to produce the observed cosmological dark matter density.

Due to their low temperature and low kinetic energy they would be undetectable.

They would be continuously emitted by the cosmological horizon in the same way as black hole radiation is continuously emitted by a black hole. Alternatively, they would arise automatically throughout the universe, whenever space grows in size.

Why is this not possible? Or why is it possible?

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Given that the answers below imply that ultra-cold neutrinos cannot be dense enough because of their fermion character, could fermion condensation (via Cooper pairs, as in superconductors) solve the problem?

This is not possible because neutrinos are fermions. If the neutrinos are very light, you need a lot of them, and because of the Pauli exclusion principle you can't pack enough in a galaxy. This is the reason for the Tremaine-Gunn bound, which rules out fermionic dark matter lighter than $$\sim1 \, \text{eV}$$.

However, there are plenty of models of dark matter involving ultralight bosons, such as axions, dilatons, hidden photons, and so on. It's perfectly possible for dark matter to be a lot of ultra-cold, ultra-light particles.

• Ok, but what about cosmological dark matter? I will edit the question to make this clearer. – Christian Jun 9 '20 at 5:01
• @Christian You mean if cold neutrinos could be a small subcomponent of the dark matter? Sure, I guess that's possible, but you could have to come up with a way to produce them -- and also a reason that would be interesting! (Note that production due to cosmological horizons does happen, but under the default rules, only ridiculously slowly in the present era, many orders of magnitude too slow to ever have any noticeable effect.) – knzhou Jun 9 '20 at 5:05
• I take your comment to mean that black hole radiation from the horizon is negligible. Is this correct? So I have a second question. Could it be that the expansion of space itself creates ultracold neutrinos? This is an almost crazy idea, triggered by a friend of a friend. – Christian Jun 9 '20 at 5:23
• @Christian That's precisely what I meant: space expansion (i.e. which leads to cosmological horizons) does create neutrinos, along with every other kind of particle, but only extremely slowly in the present era. If you want to learn to show this quantitatively, see a book on QFT in curved spacetime, such as Wald or Birrell/Davies. – knzhou Jun 9 '20 at 5:35
• @Christian what do you mean with "The question is about cosmological dark matter, not about galactic dark matter.", these are usually assumed to be the same thing (and I have a hard time seeing how they couldn't be the same thing since the densities agree) – rfl Jun 9 '20 at 6:42

No.

Neutrinos are dark matter: they are massive but don't interact with light. However, they are a very sub-dominant component. As @knzhou already correctly pointed out, the Tremaine-Gunn bound rules out that most of dark matter would be fermions with masses below approximately 1eV (such as neutrinos). Even better, observations from the Cosmic Microwave Background can be used to measure the neutrino density when the universe was 300,000 years old. One finds the density of neutrinos to be less than 0.1%. See e.g. this slightly outdated but easy-to-read discussion leading up to their equation 13.

In the context of what you are discussing, you may want to have a look at e.g. the Wikipedia article on the Cosmic Neutrino Background. This seems to be what you are referring to. That's essentially the equivalent of the Cosmic Microwave Background, but instead of photons emitted when the universe cooled so much that they could free-stream, it's neutrinos emitted when the universe cooled so much that they could free-stream.

• The cosmic neutrino background is usually said to have a temperature of around 1.95K. My question was if there could be many more neutrinos of much lower temperature, say below 1 fK, that form the cosmological dark matter density deduced by the Planck satellite. It is a crazy question, I know, and I just asked it to understand things. I thought that cosmological dark matter does not need to obey the Tremaine-Gunn bound with galactic values, but it seems that I was mistaken. – Christian Jun 9 '20 at 10:37
• Well, true, the Tremaine-Gunn bound only applies to dark matter when it is as dense as it is in (dwarf) galaxies. So there is nothing to stop you to postulate some low density of supercold neutrinos, in galaxies or elsewhere. But since that density would have to be small, it wouldn't be what most of dark matter is made of. So we wouldn't think of it in terms of dark matter then. Of course a lot of things are conceivable in science once you find your way to evade experimental constraints... – rfl Jun 9 '20 at 13:08
• I'd like to ask also here: would a fermion condensate allow to exceed the Tremaine-Gunn bound? In other words, would "neutrino-Cooper-pairs" allow higher densities? – Christian Jun 14 '20 at 10:47
• sure, the Tremaine-Gunn bound doesn't apply to bosons. – rfl Jun 15 '20 at 12:46
• @Christian what long-range interaction force between neutrinos in order to produce Cooper pairs do you envisage? It wouldn;t work in any case since the pairs can only form right at the top of the "Fermi sea". – ProfRob Nov 20 '20 at 13:25