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 $\Upsilon_\nu$ below equilibrium, i.e. $\Upsilon_\nu<1$, and the increase of the neutrino temperature $T_\nu$ via partial reheating. We establish the connection between $\Upsilon_\nu$ and $T_k$ via the modified reheating relation $T_\nu(\Upsilon_\nu)/T_\gamma$, where $T_\gamma$ is the temperature of the background radiation. Our results demonstrate that one must introduce the chemical nonequilibrium parameter, i.e., the fugacity, $\Upsilon_\nu$, as an additional standard cosmological model parameter in the evaluation of CMB fluctuations as its value allows measurement of $T_k$.