Fugacity and Reheating of Primordial Neutrinos

Abstract

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 ${{\rm Y}}_{\nu }$ below equilibrium, i.e. ${{\rm Y}}_{\nu }<1$, and the increase of the neutrino temperature $T_{\nu }$ via partial reheating. We establish the connection between ${{\rm Y}}_{\nu }$ and $T_k$ via the modified reheating relation $T_{\nu }({{\rm Y}}_{\nu })/T_{\gamma }$, 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, ${{\rm Y}}_{\nu }$, as an additional standard cosmological model parameter in the evaluation of CMB fluctuations as its value allows measurement of $T_k$.

Comments: 6 pages, 1 figure