What is wrong with the following? (Note that the question is not about galactic dark matter, but about cosmological dark matter.)

  1. Neutrinos are dark matter.

  2. A neutrino condensate would be cold. (Often, neutrinos are dismissed as being automatically hot dark matter.)

  3. Cold neutrinos could be generated continuously by the horizon. Their number would increase with time. So their density could be significant.

  4. Their temperature would be much lower than the cosmological neutrino background. The neutrino condensate would be a separate neutrino bath, much colder than the 1.95K of the CNB.

  5. A condensate (in Cooper pairs) would not encounter any density limit (in contrast to free fermions, such a warm or hot netrinos).

  6. And a cold condensate would not wash out early fluctuations (in contrast to hot neutrinos).

(7. They could also form galactic dark matter. - No, they could not, as several answers and comments pointed out.)

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/17227/2451 , physics.stackexchange.com/q/158319/2451 and links therein. $\endgroup$
    – Qmechanic
    Jun 20, 2020 at 11:31
  • $\begingroup$ I looked at those questions (and a third thread): they do not discuss neutrino condensates. In fact, a neutrino condensate seems to invalidate the answers given in both threads. Thus I made a new one. $\endgroup$ Jun 20, 2020 at 11:35
  • $\begingroup$ has not caught the mainstream arxiv.org/abs/0911.5012 , only 20 citations $\endgroup$
    – anna v
    Jun 20, 2020 at 14:18
  • 1
    $\begingroup$ see hyperphysics.phy-astr.gsu.edu/hbase/Particles/spinc.html#c4 . To make a bson two neutrinos would have to be in a bound state : in the standard model the weak interaction cannot bind two neutrinos . gravity is very very weak plus the masses of the neutrinos very small so another mechanism is needed . all I can find is new models beyond the standard model $\endgroup$
    – anna v
    Jun 22, 2020 at 10:48
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    $\begingroup$ A condensate (in Cooper pairs) would not encounter any density limit” - This is incorrect. The Pauli exclusion principle still applies to constituent particles of the pair. A super fluid is not compressible. Thus your condensate argument is moot and no different from individual neutrinos, but +1 for trying :) $\endgroup$
    – safesphere
    Jun 26, 2020 at 4:44

1 Answer 1


A neutrino condensate would involve lowering the energy of a pair of neutrinos. The only particles that could participate in such interactions would be those that are already at the top of a degenerate "Fermi sea" of neutrinos. In other words the formation of pairs would have the effect of "squaring off" the occupation index distribution and leaving a small gap between the top of the Fermi sea and a small number of higher energy neutrinos; in much the same way that pair-forming in neutron stars only acts on the small fraction of neutrons with the highest energies.

As such, there would be almost no effect on the bulk dynamics of the neutrino fluid and the Tremaine-Gunn (1979) restriction on forming galaxy halos from light leptons would still be a problem. The bulk of the neutrino fluid would still be degenerate and it would be impossible to pack enough light neutrinos into the available phase space.

Aside from this - what is the long-range pair-forming interaction that can work between particles that only interact via the short-range weak force. Gravity? Two neutrinos separated by $10^{-5}$ m (from the number density of ~0.1 eV neutrinos needed to explain galaxy halos) have a gravitational potential energy of $\sim 10^{-23}$ eV. So they would have to be colder than $10^{-19}$ K to avoid the pairs being thermally broken.

If the neutrinos are just meant to contribute to some general background rather than to galaxy halos then the question arises - why wouldn't they concentrate in galaxy halos in the same way? In any case the universal average density of dark matter would suggest a neutrino number density (assuming the same rest mass) about 3-4 orders of magnitude lower than the concentrations in galactic halos. This changes the average separation to $10^{-4}$ m and thus the pairs would have to be colder than $10^{-18}$ K.

I don't see the merit of this hypothesis if the proposed dark matter doesn't actually explain most of the problems that dark matter is required for - i.e. galaxy and cluster dynamics and point #5 is incorrect (as well as #7 that was originally part of the question I answered).

  • $\begingroup$ This is true. But the question was about cosmological dark matter, not about galactic dark matter. And cosmological dark matter/beutrinos could be as cold as $10^{-30} K$. $\endgroup$ Nov 24, 2020 at 14:21
  • $\begingroup$ @Christian I'm not following. There needs to be >10 times as much dark matter as luminous matter in our Galaxy. This is roughly, though a little lower than the ratio of luminous matter to dark matter in the cosmos. Are you therefore suggesting that there are two forms of dark matter? $\endgroup$
    – ProfRob
    Nov 24, 2020 at 15:17

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