Relic Neutrino Freeze-out: Dependence on Natural Constants

Analysis of cosmic microwave background radiation fluctuations favors an effective number of neutrinos, $N_\nu>3$. This motivates a reinvestigation of the neutrino freeze-out process. Here we characterize the dependence of $N_\nu$ on the Standard Model (SM) parameters that govern neutrino freeze-out. We show that $N_\nu$ depends on a combination $\eta$ of several natural constants characterizing the relative strength of weak interaction processes in the early Universe and on the Weinberg angle $\sin^2\theta_W$. We determine numerically the dependence $N_\nu(\eta,\sin^2\theta_W)$ and discuss these results. The extensive numerical computations are made possible by two novel numerical procedures: a spectral method Boltzmann equation solver adapted to allow emerging chemical non-equilibrium, and a method to evaluate Boltzmann equation collision integrals that generates a smooth integrand.