Neutrino decoupling including flavour oscillations and primordial nucleosynthesis (2008.01074v2)

Abstract: We revisit the decoupling of neutrinos in the early universe with flavour oscillations. We rederive the quantum kinetic equations which determine the neutrino evolution based on a BBGKY-like hierarchy, and include for the first time the full collision term, with both on- and off-diagonal terms for all relevant reactions. We focus on the case of zero chemical potential and solve these equations numerically. We also develop an approximate scheme based on the adiabatic evolution in the matter basis. In fact, the large difference between the oscillations and cosmological time scales allows to consider averaged flavour oscillations which can speed up the numerical integration by two orders of magnitude, when combined with a direct computation of the differential system Jacobian. The approximate numerical scheme is also useful to gain more insight into the physics of neutrino decoupling. Including the most recent results on plasma thermodynamics QED corrections, we update the effective number of neutrinos to $N_{\mathrm{eff}} = 3.0440$. Finally we study the impact of flavour oscillations during neutrino decoupling on the subsequent primordial nucleosynthesis.

• The paper refines neutrino decoupling by integrating flavour oscillations within detailed quantum kinetic equations, leading to an updated effective neutrino number of 3.0440.
• It achieves methodological advances by accurately addressing both diagonal and off-diagonal collision terms, thereby capturing non-thermal spectral distortions.
• The refined treatment of neutrino interactions strongly impacts primordial nucleosynthesis, aligning light element production with observed abundance patterns.

Neutrino Decoupling Including Flavour Oscillations and Primordial Nucleosynthesis

The paper presented by Froustey, Pitrou, and Volpe revisits the decoupling of neutrinos in the early universe to incorporate the impact of flavour oscillations. By extending previous work on quantum kinetic equations (QKEs) for neutrino evolution amid a primordial nucleosynthesis environment, the authors address a gap in accurately considering both on-diagonal and off-diagonal collision terms. Their work achieves a refined prediction of the effective number of neutrinos, $N_{\rm eff}$, a parameter crucial for understanding energy density during the Cosmic Microwave Background (CMB) epoch.

Methodological Advancements

The authors start by deriving comprehensive QKEs using a BBGKY-like hierarchy approach, a robust formalism allowing detailed tracing of neutrino evolutions. The process includes meticulous treatment of flavour oscillations and interactions. Notably, they account for neutrino self-interactions with their full matrix structure, sidestepping approximations employed in earlier works that neglected off-diagonal collision terms. This paper impressively achieves computational advances by implementing an adiabatic approximation, which combines efficient integration strategies to reduce numerical integration time markedly.

Main Findings

1. Effective Number of Neutrinos: The paper updates $N_{\rm eff}$ to $3.0440$ when accounting for QED corrections in the plasma environment, an enhancement to prior estimations. This precision update stems from incorporating flavour oscillations fully and considering recent advances in our understanding of the early universe thermodynamics.
2. Neutrino Spectra Distortions: Considerable focus is placed on deriving the non-thermal spectral distortions effectively. Oscillations induce a reduction in the electron-type neutrinos' reheating but increase the spectra for other flavours, underlining the importance of flavour oscillation beyond diagonal approximations.
3. Implications on Primordial Nucleosynthesis: The nuanced view of neutrino interactions and oscillations has tangible implications on neutron/proton freeze-out, influencing the production ratios of light elements such as deuterium and helium. The clock effect, increased by a higher $N_{\rm eff}$, substantiates these variations, ensuring consistency with observed primordial abundance patterns.

Future Directions and Implications

This comprehensive treatment augurs well for theoretical and observational cosmology. By refining the understanding of neutrino decoupling, this research not only narrows constraints on cosmological models but also furnishes groundwork for future high-precision experiments, such as those from CMB observatories. Intriguingly, their approach hints at the potential for future explorations into non-standard physics, such as hypothetical neutrino self-interactions or CP-violating processes, setting a benchmark for more extended theoretical frameworks.

In conclusion, this paper exemplifies the importance of rigorous inclusion of flavour oscillations in cosmological neutrino dynamics, crucially contributing to the accurate prediction of cosmological parameters. As new data emerge, particularly from neutrino mass hierarchy investigations, these insights will be vital in fine-tuning our understanding of the universe's infancy.