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Multi-momentum and multi-flavour active-sterile neutrino oscillations in the early universe: role of neutrino asymmetries and effects on nucleosynthesis

Ninetta Saviano, Alessandro Mirizzi, Ofelia Pisanti, Pasquale Dario Serpico, Gianpiero Mangano, Gennaro Miele

TL;DR

This work tackles the cosmological implications of eV-scale sterile neutrinos suggested by short-baseline anomalies by solving multi-flavour, multi-momentum active-sterile oscillation kinetics in the early universe. The authors develop a density-matrix formalism with dimensionless variables $x$, $y$, $z$ and EoMs for $\rho$ and $\bar{\rho}$ that include vacuum mixing via ${\mathcal U}$, matter effects, and collisions, initialized with degeneracy parameters $\xi_e$ and $\xi_\mu$. They find that a full multi-momentum treatment enhances sterile production by up to about $0.2$ in $N_{ m eff}$ compared to the average-momentum approximation, pushing the required lepton asymmetries to $|L_\nu| \gtrsim 10^{-2}$ to suppress thermalization. Large asymmetries also induce distortions in the electron-neutrino spectra, feeding into significant changes in BBN yields such as $Y_p$ and $^2$H/H, and can lead to a lower $N_{ m eff}$ at CMB epochs despite larger $Y_p$. These results refine the cosmological viability of light sterile neutrinos and highlight the need for precision, high-resolution cosmological analyses when confronting short-baseline hints with Planck-era data.

Abstract

We perform a study of the flavour evolution in the early universe of a multi-flavour active-sterile neutrino system with parameters inspired by the short-baseline neutrino anomalies. In a neutrino-symmetric bath a "thermal" population of the sterile state would quickly grow, but in the presence of primordial neutrino asymmetries a self-suppression as well as a resonant sterile neutrino production can take place, depending on temperature and chosen parameters. In order to characterize these effects, we go beyond the usual average momentum and single mixing approximations and consider a multi-momentum and multi-flavour treatment of the kinetic equations. We find that the enhancement obtained in this case with respect to the average momentum approximation is significant, up to \sim 20 % of a degree of freedom. Such detailed and computationally demanding treatment further raises the asymmetry values required to significantly suppress the sterile neutrino production, up to large and preferentially net asymmetries |L_ν| > O(10^{-2}). For such asymmetries, however, the active-sterile flavour conversions happen so late that significant distortions are produced in the electron (anti)neutrino spectra. The larger |L_ν|, the more the impact of these distortions takes over as dominant cosmological effect, notably increasing the 4 He abundance in primordial nucleosynthesis (BBN). The standard expression of the primordial yields in terms of the effective number of neutrinos and asymmetries is also greatly altered. We numerically estimate the magnitude of such effects for a few representative cases and comment on possible implications for forthcoming cosmological measurements.

Multi-momentum and multi-flavour active-sterile neutrino oscillations in the early universe: role of neutrino asymmetries and effects on nucleosynthesis

TL;DR

This work tackles the cosmological implications of eV-scale sterile neutrinos suggested by short-baseline anomalies by solving multi-flavour, multi-momentum active-sterile oscillation kinetics in the early universe. The authors develop a density-matrix formalism with dimensionless variables , , and EoMs for and that include vacuum mixing via , matter effects, and collisions, initialized with degeneracy parameters and . They find that a full multi-momentum treatment enhances sterile production by up to about in compared to the average-momentum approximation, pushing the required lepton asymmetries to to suppress thermalization. Large asymmetries also induce distortions in the electron-neutrino spectra, feeding into significant changes in BBN yields such as and H/H, and can lead to a lower at CMB epochs despite larger . These results refine the cosmological viability of light sterile neutrinos and highlight the need for precision, high-resolution cosmological analyses when confronting short-baseline hints with Planck-era data.

Abstract

We perform a study of the flavour evolution in the early universe of a multi-flavour active-sterile neutrino system with parameters inspired by the short-baseline neutrino anomalies. In a neutrino-symmetric bath a "thermal" population of the sterile state would quickly grow, but in the presence of primordial neutrino asymmetries a self-suppression as well as a resonant sterile neutrino production can take place, depending on temperature and chosen parameters. In order to characterize these effects, we go beyond the usual average momentum and single mixing approximations and consider a multi-momentum and multi-flavour treatment of the kinetic equations. We find that the enhancement obtained in this case with respect to the average momentum approximation is significant, up to \sim 20 % of a degree of freedom. Such detailed and computationally demanding treatment further raises the asymmetry values required to significantly suppress the sterile neutrino production, up to large and preferentially net asymmetries |L_ν| > O(10^{-2}). For such asymmetries, however, the active-sterile flavour conversions happen so late that significant distortions are produced in the electron (anti)neutrino spectra. The larger |L_ν|, the more the impact of these distortions takes over as dominant cosmological effect, notably increasing the 4 He abundance in primordial nucleosynthesis (BBN). The standard expression of the primordial yields in terms of the effective number of neutrinos and asymmetries is also greatly altered. We numerically estimate the magnitude of such effects for a few representative cases and comment on possible implications for forthcoming cosmological measurements.

Paper Structure

This paper contains 6 sections, 14 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Multi-momentum flavour evolution
  3. Equations of motion
  4. Results
  5. Impact on observables: $N_{\rm eff}$ and light nuclei abundances
  6. Conclusions

Figures (4)

  • Figure 1: Evolution of the total value of the sterile neutrino density matrix element $\rho_{ss}$ as function of the temperature $T$ for the multi-momentum case (continuos curves) and the average momentum (dot-dashed curves) case with a thermal momentum $\langle y \rangle=3.15$. Left panels correspond to $\xi_e=\xi_\mu$, while in the lowers $\xi_e=-\xi_\mu$. Upper panels refer to $\xi_e=10^{-3}$ and right to $\xi_e=10^{-2}$.
  • Figure 2: Cases with $\xi_{e}= 10^{-3}$. Upper panels: Final $\nu_{e}$ energy spectra at $T= 1$ MeV (dashed curve) and initial ones (continuous curve). Lower panel: Ratio $R$ between final and initial $\nu_{e}$ energy spectra. Left panels refer to $\xi_{e}= \xi_{\mu}$ while right panels are for $\xi_{e}= -\xi_{\mu}$.
  • Figure 3: Cases with $\xi_{e}= 10^{-2}$. Upper panels: Final $\nu_{e}$ energy spectra at $T= 1$ MeV (dashed curve) and initial ones (continuous curve). Lower panel: Ratio $R$ between final and initial $\nu_{e}$ energy spectra. Left panels refer to $\xi_{e}= \xi_{\mu}$ while right panels are for $\xi_{e}= -\xi_{\mu}$.
  • Figure 4: Evolution of $\Delta N_{\rm eff}$ vs. temperature $T$ for equal asymmetries $\xi_e=\xi_\mu$ (left panel) and opposite asymmetries $\xi_e=-\xi_\mu$ (right panel). Solid curves refer to $\xi_e=10^{-3}$ while dashed curves are for $\xi_e=10^{-2}$.