Continuing on from the cool physics Q&A'd on the threads Where are all the slow neutrinos?, Is it possible that all "spontaneous nuclear decay" is actually "slow neutrino" induced?, and What does the cosmic neutrino background look like today, given that neutrinos possess mass?, I have a follow-up question that stems from this answer to that last question.
More specifically, the Big Bang must have produced a bunch of neutrinos and antineutrinos as a side-effect of the creation of all that matter, and past a certain point these would decouple from matter and just fly on unimpeded through space. Over time, these neutrinos would get redshifted just like the cosmic microwave background did, to form a Cosmic Neutrino Background at a temperature of around $1.9\:\mathrm K$.
Depending on the neutrino masses, this could mean a range of velocities, but if the neutrinos are relatively massive, to quote rob's answer, they
would have typical speeds of under 100 km/s, slower than the escape velocity of some stars. Cold neutrinos might therefore accumulate in gravitational wells, resulting in substantial density enhancement over the 100 ν/cm³ average you expect over intergalactic space.
Now, about this accumulation in gravitational wells, I have a question similar to rob's later comment,
(I'm just the tiniest bit murky on how the cold neutrinos get trapped without scattering, but I'm prepared to believe it's discussed in the literature.)
In contrast, I'm completely in the dark on how the cold neutrinos get trapped without scattering. You've got this small particle, that only interacts gravitationally, coming in towards a star with a velocity at infinity of the order of (but smaller than) the escape velocity. Under normal circumstances, the particle will approach the star... and whizz off again, in a hyperbolic trajectory that ends up with the same asymptotic velocity it came in with. If there's a third body to interact with, it might get deflected into a bound orbit, but with no meaningful interactions but gravity this seems very unlikely to me to work on astronomically large numbers of neutrinos.
What are the rough physics behind the capture of these massive cold neutrinos in a gravitational well?