A precision calculation of relic neutrino decoupling

Abstract

We study the distortions of equilibrium spectra of relic neutrinos due to the interactions with electrons, positrons, and neutrinos in the early Universe. We solve the integro-differential kinetic equations for the neutrino density matrix, including three-flavor oscillations and finite temperature corrections from QED up to the next-to-leading order $\mathcal{O}(e^3)$ for the first time. In addition, the equivalent kinetic equations in the mass basis of neutrinos are directly solved, and we numerically evaluate the distortions of the neutrino spectra in the mass basis as well, which can be easily extrapolated into those for non-relativistic neutrinos in the current Universe. In both bases, we find the same value of the effective number of neutrinos, $N_{\mathrm{eff}}=3.044$, which parameterizes the total neutrino energy density. The estimated error for the value of $N_{\mathrm{eff}}$ due to the numerical calculations and the choice of neutrino mixing parameters would be at most 0.0005.

31 pages, 5 figures and 4 tables, accepted JCAP version

References in corpus (7)

• Relic neutrino decoupling with flavour oscillations revisited
• SPT-3G: A Next-Generation Cosmic Microwave Background Polarization Experiment on the South Pole Telescope
• Thermalisation of sterile neutrinos in the early Universe in the 3+1 scheme with full mixing matrix
• Cosmological lepton asymmetry with a nonzero mixing angle θ_{13}
• Relic Neutrino Freeze-out: Dependence on Natural Constants
• Incomplete neutrino decoupling effect on big bang nucleosynthesis
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• Two sides of the same coin: sterile neutrinos and dark radiation. Status and perspectives
• Gravitational waves from first-order phase transitions in Majoron models of neutrino mass