A review of neutrino decoupling from the early universe to the current universe

TL;DR

This paper reviews neutrino decoupling in the early universe, solving complex equations to understand spectral distortions and their impact on the cosmic neutrino background and detection experiments, providing a precise value for N_eff.

Contribution

It introduces a detailed kinetic equation approach including flavor oscillations and finite temperature corrections, refining the estimate of N_eff and highlighting neglected effects.

Findings

Estimated N_eff as 3.044 with high precision

Quantified spectral distortions' effects on neutrino density and energy

Discussed implications for direct detection experiments like PTOLEMY

Abstract

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 $N_{\rm eff}$.