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The neutrinos from the cosmic neutrino background have a temperature of $T_\nu=1.945K$, that is an energy of $E=\frac{3}{2}k_BT_\nu$. If the neutrino's mass is around $0.1eV$

$$ \frac{3}{2}k_BT_\nu<m_\nu c^2 $$

Why it is considered relativistic if the rest mass is larger than the energy?

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From neutrino oscillation experiments, we know that there are three neutrino mass eigenstates whose masses are all different, and we know roughly the size of those differences (squared). This sets a lower limit on the mass of the heaviest neutrino. But we have no data on the mass of the lightest neutrino. It is possible, for instance, that there are two massive and one massless neutrino.

Your calculation argues that at least one neutrino species should be non-relativistic at the current C$\nu$B temperature. But the lightest neutrino may still be relativistic.

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    $\begingroup$ I thought they have to have a mass, since we can observe neutrino oscillations $\endgroup$
    – Javier
    Commented Jun 2, 2022 at 14:38
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    $\begingroup$ @Javier Neutrino oscillation implies that the masses of the three neutrino species are all different. That means they can't all be zero, but there's nothing which says that one of them can't be. $\endgroup$
    – J. Murray
    Commented Jun 2, 2022 at 15:27
  • $\begingroup$ @Javier see also this answer: physics.stackexchange.com/a/15483/226902 $\endgroup$
    – Quillo
    Commented Jun 2, 2022 at 16:03
  • $\begingroup$ @J.Murray Thank you! $\endgroup$
    – Javier
    Commented Jun 2, 2022 at 16:04

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