Relic neutrino decoupling with flavour oscillations revisited (1606.06986v1)

Abstract: We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, N_eff. We find a value of N_eff=3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that N_eff can be reduced down to 3.040 or enhanced up to 3.059.

• The paper advances neutrino decoupling models by integrating complete collision terms into momentum-dependent kinetic equations.
• It confirms that three-flavour oscillations and neutrino mass hierarchies yield an effective neutrino number N_eff of approximately 3.045.
• The study explores non-standard neutrino-electron interactions, indicating only minor adjustments in N_eff that align with theoretical predictions.

Relic Neutrino Decoupling with Flavour Oscillations Revisited: An Analysis

The research paper "Relic Neutrino Decoupling with Flavour Oscillations Revisited" authored by Pablo F. de Salas and Sergio Pastor addresses the nuanced mechanisms involved in the decoupling of neutrinos in the early universe, with a specific focus on the impact of three-flavour oscillations within the cosmic framework. The paper brings forth a comprehensive evaluation of the evolution of neutrino spectra by refining the established models through the integration of complete collision terms in the kinetic equations pertinent to neutrino density matrices. The meticulous analysis carried out does not result in a modification of the effective number of neutrinos, $N_{\rm eff}$, which remains at approximately 3.045 in consonance with preceding theoretical assessments and compatible with contemporary Planck data evaluations.

Key Findings and Methodology

1. Improved Collision Integration:
   • This paper distinguishes itself by solving the momentum-dependent kinetic equations while incorporating full collision integrals for both diagonal and off-diagonal components of the neutrino density matrix. This approach contrasts earlier studies that utilized simplified damping terms for off-diagonal elements.
   • The research underscores altered evolution patterns of off-diagonal elements but confirms that these do not influence the final value of $N_{\rm eff}$.
2. Consistency Across Mass Hierarchies:
   • The paper evaluates the effects of different neutrino mass hierarchies (normal and inverted) on $N_{\rm eff}$, concluding that the mass ordering does not materially affect the contributions of neutrinos to the radiation energy density, reaffirming $N_{\rm eff} = 3.045$.
3. Inclusion of Non-Standard Interactions:
   • The paper extends its scope to explore potential deviations introduced by non-standard neutrino-electron interactions (NSI), as hypothesized by extended theoretical models accommodating neutrino mass. It finds minor alterations, with $N_{\rm eff}$ adjusting between 3.040 and 3.059 under the influence of permissible NSI parameters.

Implications and Future Directions

The implications of this in-depth reassessment extend into both theoretical comprehension and the practicalities of cosmological models:

• Standard Model Reference: By confirming the standard model's expectation for $N_{\rm eff}$, the paper solidifies baselines used in broader cosmological explorations and validates the continued use of these parameters in corresponding data analyses.
• Precision in Future Cosmological Studies: With an eye toward future precision cosmological surveys, such disambiguated and precise modeling enhances the reliability of neutrino-related data in validating or challenging broader cosmological frameworks.
• Impacts on New Physics: The exploration into NSI provides valuable constraints and clarifications for theories beyond the standard model, where neutrino masses play a crucial role. This, in turn, propels further examination into the feasible parameter space of new physics models.

This paper serves as an important incremental step in the intricate understanding of relic neutrinos' roles within the universe's early thermal history. The quantitative rigour introduced by comprehensively addressing collision terms showcases a template for future work in the domain, possibly extending into areas where the repercussions of neutrino behaviors intersect with dark matter and energy densities in the universe. Such refined models underscore the necessity for precision cosmology as the field progresses with greater observational accuracies anticipated from upcoming cosmic microwave background (CMB) experiments.