According to Wikipedia, neutrinos separated from other matter seconds after the Big Bang and formed a separate background radiation field which now fills space at a temperature ~2 K.
Supposing neutrinos have a rest mass of 2 eV/c2, they should be traveling at an average speed
$$v_\nu = c \sqrt{2 \cdot k \cdot \frac{2\mathrm{K}}{2 \mathrm{eV}}} \approx 4 \cdot 10^6 \mathrm{m/s}$$
Seems to me that as neutrinos slow down due to the metric expansion of space, they should be clustering into orbits around galaxies. Distant galaxies should show the effect less because the neutrinos were going faster at the time.
Is this correct?
According to the same Wikipedia article, the background neutrinos originally had an energy of 2.5 MeV and were in thermal equilibrium with electrons, positrons, and photons. So whereas they once accounted for a quarter of the mass-energy of the Universe (or half, because there are three flavors?), their current, essentially rest mass is less than a millionth of it.
That's too little to put a dent in the dark matter mystery, or even observe the time-dependent effect I just mentioned, right?
Also, galactic orbits aren't metrically expanding so this essentially traps the neutrinos around any galaxy into a spherical shell with the orbital radius and speed dependent on the galaxy mass. A neutrino which is going too fast will escape and pass a galaxy, but by the time it reaches the next galaxy, it will be further redshifted, and might be gravitationally trapped. Then it won't slow down any further because the neighborhood of a galaxy is geometrically stable.
If there were something larger for neutrinos to orbit, they could stabilize at a higher speed, but it still couldn't be relativistic, right?
Since nothing (besides lots of empty space) can slow down a neutrino, this sets a lower speed limit on all neutrinos in a galaxy or galaxy cluster, right?