Relic Neutrino Freeze-out: Dependence on Natural Constants

Analysis of cosmic microwave background radiation fluctuations favors an effective number of neutrinos, $N_ν>3$. This motivates a reinvestigation of the neutrino freeze-out process. Here we characterize the dependence of $N_ν$ on the Standard Model (SM) parameters that govern neutrino freeze-out. We show that $N_ν$ depends on a combination $η$ of several natural constants characterizing the relative strength of weak interaction processes in the early Universe and on the Weinberg angle $\sin^2θ_W$. We determine numerically the dependence $N_ν(η,\sin^2θ_W)$ 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.

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