## Relativistic at freeze out? Definition of HDM

Okay so in a HDM scenario, I have seen it described that the neutrinos were relativistic at freeze out. (If I could find it I would reference it.)

The condition for relativistic travel is E>>m but just before freezeout, the neutrino has energy equal to the thermal energy of the universe (as it is in thermal equilibrium). Since the particle freezes out when the energy of the universe $\approx$ the mass of the particle, then just before freeze out the particle is not relativistic! Correct?

Dan

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Mentor
 Since the particle freezes out when the energy of the universe ≈ the mass of the particle
Why? I don't think this is true.

 Quote by cohen990 Okay so in a HDM scenario, I have seen it described that the neutrinos were relativistic at freeze out. (If I could find it I would reference it.) Is this a contradictory statement? The condition for relativistic travel is E>>m but just before freezeout, the neutrino has energy equal to the thermal energy of the universe (as it is in thermal equilibrium). Since the particle freezes out when the energy of the universe $\approx$ the mass of the particle, then just before freeze out the particle is not relativistic! Correct? Anyway, thanks for your time, Dan
I don't really know if this is what you asking, but if what you are talking about is something like the neutrino background of the universe (analogue to the CMB), then neutrinos 'decouple' (getting away from this thermal equilibrium soup) from matter when the universe was still incredibly hot. Therefore these neutrinos were relativistic when they escaped. But as of today, due to cosmological redshifts, their temperature is something around the CMB.