A Review of Neutrino Decoupling from the Early Universe to the Current Universe

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 O(e3). 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 (CνB) in the current universe, and discuss the implications of these effects on the capture rates in direct detection of the CνB on tritium, with emphasis on the PTOLEMY-type experiment. In addition, we find a precise value of the effective number of neutrinos, Neff=3.044. However, QED corrections to weak interaction rates at order O(e2GF2) 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 ±(10−3−10−4) in Neff.

Non-unitary three-neutrino mixing in the early Universe

“…The role of neutrinos is encoded in the effective number of relativistic species N eff , which quantifies relativistic degrees of freedom different from photons that contribute to the cosmological radiation density. Within the canonical picture of neutrino decoupling, its value after neutrino decoupling is N eff = 3.0440 [26][27][28][29], in excellent agreement with the most recent determination from the combination of several cosmological probes, N eff = 2.99 +0. 34 −0.33 at 95% confidence level (CL) from Planck 2018 (TT, TE, EE + lowE + lensing + BAO) [30].…”

Phase transitions and gravitational waves in a model of ℤ3 scalar dark matter

“…The following values for the aforementioned parameters allows us to compute the factor F gw,0 [150,151]: where N eff = 3.044 [152] has been used in the computation of g s0 and g 0 . Note that g s0 ≃ 3.91 and g 0 = 2 are considered in refs.…”

Theoretical and Experimental Challenges in the Measurement of Neutrino Mass

“…The neutrino to photon energy density ratio (ρ ν /ρ γ ) between the e − e + annihilation time and nonrelativistic transition time of neutrino can be given by the expression ρ ν /ρ γ = 7/8 N eff 4/11 4/3 , where N eff is the effective number of neutrinos estimated as 3.044 from a detailed calculations of the process of neutrino decoupling with at least 10 −4 numerical precision [13][14][15][16]. The direct measurement of the invisible width of Z-boson limits the number of active left-handed neutrino states to three, N ν = 2 9963 ± 0 0074, and they are ν e , ν μ , ν τ [17].…”