A precision calculation of relic neutrino decoupling (2005.07047v2)

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, $N_{\rm eff} = 3.044$, which parameterizes the total neutrino energy density. The estimated error for the value of $N_{\rm eff}$ due to the numerical calculations and the choice of neutrino mixing parameters would be at most 0.0005.

• The paper presents a precise computation of relic neutrino decoupling by solving full Boltzmann kinetic equations accounting for three-flavor oscillations.
• It incorporates next-to-leading order finite temperature QED corrections that refine the Nₑff determination to 3.044 with a 0.0005 error margin.
• The dual analysis in flavor and mass bases offers a robust framework to guide future CMB and BBN experiments in probing early Universe neutrino properties.

Precision Calculation of Relic Neutrino Decoupling

The paper by Kensuke Akita and Masahide Yamaguchi constitutes a detailed numerical paper of relic neutrino decoupling in the early Universe, incorporating three-flavor oscillations and finite temperature corrections up to the next-to-leading order in quantum electrodynamics (QED). Their key contribution includes solving the integro-differential kinetic equations for neutrino density matrices, both in the flavor and mass bases, to achieve a more precise determination of the effective number of neutrinos ($N_{\rm eff}$) with a reported value of $N_{\rm eff} = 3.044$, and an estimated error margin of $0.0005$.

Key Findings and Methodology

1. Methodological Framework: The authors utilize a comprehensive approach involving the full Boltzmann equations for neutrino density matrices, factoring in interactions with electrons, positrons, and other neutrinos. They solved these equations using a discretization method, complemented by robust computational techniques to ensure convergence.
2. Finite Temperature QED Corrections: The paper incorporates QED corrections to the electron mass, contributing significantly to the precision of $N_{\rm eff}$. By accounting for these corrections up to $\mathcal{O}(e^3)$, the investigation provides insights into their influence on early Universe thermodynamics.
3. Neutrino Oscillations and QED Impact: The paper highlights the subtle increase in $N_{\rm eff}$ due to neutrino mixing and oscillations. Conversely, the paper details how higher-order QED corrections slightly decrease $N_{\rm eff}$; a delicate balance captured numerically here for the first time at this precision level.
4. Efficacy of Mass Basis Analysis: The authors present the Boltzmann equations in the mass basis, considering neutrinos as mass eigenstates, which allows for straightforward extrapolation to the present epoch. This effectively supports future experimental efforts aimed at detecting relic neutrinos as massive rather than flavor particles.

Implications and Future Directions

The results imply a nuanced understanding of neutrino decoupling processes in the early Universe, impacting constraints on cosmic background models and broader cosmological parameters. The precise value of $N_{\rm eff}$ and detailed characterization of neutrino spectra enrich the validation framework for cosmological phenomena observed through Cosmic Microwave Background (CMB) anisotropies and Big Bang Nucleosynthesis (BBN).

Going forward, the methodologies elucidated in this paper can inform analytical approaches in next-generation CMB experiments, which aspire to achieve sub-percent precision in measuring cosmological neutrino parameters. Moreover, this work sets a precedent for incorporating ever more precise higher-order corrections in quantum field theoretical treatments of the early Universe.

In conclusion, the paper delivers a meticulous account of relic neutrino decoupling, bridging significant gaps between theoretical predictions and observational cosmology. Its detailed analysis offers a template for further explorations of neutrino properties and their cosmological implications, serving as a foundational reference for continued interdisciplinary advances in the field.