= Degenerate neutrino and antineutrino energy density
{title2=$\rho_\nu+\rho_{\bar\nu}\simeq|\mu_\nu|^4/(8\pi^2)$}
For one massless <neutrino> flavor with one helicity per member and $|\mu_\nu|\gg T_\nu$, the <Fermi-Dirac distribution> fills momentum states up to the positive <chemical potential>. If $\mu_\nu>0$, the <neutrino> density is $\mu_\nu^4/(8\pi^2)$ and the <antineutrino> contribution is approximately $3T_\nu^4e^{-\mu_\nu/T_\nu}/\pi^2$. For negative <chemical potential> the roles reverse. Thus the leading total <energy density> is even in $\mu_\nu$ and has no factor of two from the two species. Extra populated internal degrees of freedom do multiply it. This distinction prevents using a positive-degeneracy approximation for an exponentially dilute negative-chemical-potential distribution.
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