Fugacity and Reheating of Primordial Neutrinos

We clarify in a quantitative way the impact that distinct chemical $T_c$ and kinetic $T_k$ freeze-out temperatures have on the reduction of the neutrino fugacity $Υ_ν$ below equilibrium, i.e. $Υ_ν<1$, and the increase of the neutrino temperature $T_ν$ via partial reheating. We establish the connection between $Υ_ν$ and $T_k$ via the modified reheating relation $T_ν(Υ_ν)/T_γ$, where $T_γ$ is the temperature of the background radiation. Our results demonstrate that one must introduce the chemical nonequilibrium parameter, i.e., the fugacity, $Υ_ν$, as an additional standard cosmological model parameter in the evaluation of CMB fluctuations as its value allows measurement of $T_k$.

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