Timeline for What mass do neutrinos have in the early universe?
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| Dec 12, 2023 at 17:06 | comment | added | J.G. | We sum over energy states but, holding $p$ fixed, that's equivalent to mass states. Writing $E_i=\sqrt{m_i^2+p^2}$,$$Z(p,\,T)=\prod_i\left(1+e^{-E_i/T}\right)\implies f(p,\,T)=\sum_i\frac{1}{e^{E_i/T}+1}.$$ | |
| Dec 12, 2023 at 16:46 | comment | added | user268009 | If you can elaborate on that it would be great, since it makes sense to tackle the question from first principles. But again, when computing the partition function one usually sums over energy states, so we have again the same problem... | |
| Nov 30, 2023 at 17:36 | comment | added | J.G. | You can't just plug in a value of $E$. You have to derive $f=\langle N\rangle$ from first principles from a partition function over all mass eigenstates. Presumably, since you can have neutrinos in all three of them, you should multiply three PFs, thus adding three $f$s obtained by log-differentiation. | |
| Nov 30, 2023 at 17:23 | history | edited | Qmechanic♦ |
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| Nov 30, 2023 at 16:48 | history | asked | user268009 | CC BY-SA 4.0 |