http://arxiv.org/abs/2210.10307
We review the distortions of spectra of relic neutrinos due to the interactions with electrons, positrons, and neutrinos in the early universe. We solve integro-differential kinetic equations for the neutrino density matrix, including vacuum three-flavor neutrino oscillations, oscillations in electron and positron background, a collision term and finite temperature corrections to electron mass and electromagnetic plasma up to the next-to-leading order $\mathcal{O}(e^3)$. After that, we estimate the effects of the spectral distortions in neutrino decoupling on the number density and energy density of the Cosmic Neutrino Background (C$\nu$B) in the current universe, and discuss the implications of these effects on the capture rates in direct detection of the C$\nu$B on tritium, with emphasis on the PTOLEMY-type experiment. In addition, we find a precise value of the effective number of neutrinos, $N_{\rm eff}=3.044$. However, QED corrections to weak interaction rates at order $\mathcal{O}(e^2 G_F^2)$ and forward scattering of neutrinos via their self-interactions have not been precisely taken into account in the whole literature so far. Recent studies suggest that these neglections might induce uncertainties of $\pm(10^{-3} – 10^{-4})$ in $N_{\rm eff}$.
K. Akita and M. Yamaguchi
Thu, 20 Oct 22
18/74
Comments: 68 pages, 5 figures, 9 tables; comments welcome; invited review submitted in Universe, special issue “Recent Advances in Neutrino Physics: From Theory to Experiments”
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