Neutrino degeneracy parameter (${\xi }_{\nu }$)

The neutrino degeneracy parameter is the dimensionless chemical potentialIn thermal equilibrium the corresponding antineutrino has chemical potential $-{\mu }_{\nu }$.

A degenerate relic neutrino has ${\xi }_{\nu }\gg 1$. In the ultrarelativistic limit its Fermi-Dirac distribution approaches a filled momentum sphere, giving for one internal statewhile the antineutrino density is exponentially suppressed.

A nonzero neutrino chemical potential produces unequal neutrino and antineutrino densities and hence a cosmological lepton asymmetry. It changes the radiation density, and an electron-neutrino asymmetry also changes neutron--proton weak equilibrium during Big Bang nucleosynthesis.