Relic density of neutrinos with primordial asymmetries

TL;DR

The degree of flavor equilibration among neutrinos and with the ambient plasma is estimated for the first time, and the restrictive big-bang nucleosynthesis bound on the nu_{e}nu[over]_{e] asymmetry indeed applies to all flavors.

Abstract

We study flavor oscillations in the early universe, assuming primordial neutrino-antineutrino asymmetries. Including collisions and pair processes in the kinetic equations, we not only estimate the degree of flavor equilibration, but for the first time also kinetic equilibration among neutrinos and with the ambient plasma. Typically the restrictive BBN bound on the nue-antinue asymmetry indeed applies to all flavors as claimed in the previous literature, but fine-tuned initial asymmetries always allow for a large surviving neutrino excess radiation that may show up in precision cosmological data.

Figures (3)

• Figure 1: Evolution of the neutrino energy density. The vertical axis is marked with $N_{\rm eff}$, left before $e^+e^-$ annihilation, right afterwards. Dotted lines: Baseline case without asymmetries. Top panel: $\theta_{13}=0$, the solid lines correspond to $\sin^2\theta_{12}=0$, 0.1, $0.3$, and 0.5 from top to bottom. Bottom panel:$\sin^2\theta_{12}=0.3$, the top solid curve is $\sin^2\theta_{13}=0$, while the other solid curves correspond to $\sin^2\theta_{13}=0.04$ with normal (top) and inverted (bottom) hierarchy.
• Figure 2: Final $\nu_e$ and $\bar{\nu}_e$ spectra for $\theta_{13}=0$ and $\sin^2\theta_{12}=0.3$. The dotted lines are Fermi-Dirac spectra producing the same $\nu_e\bar{\nu}_e$ asymmetry and the same energy density $\rho_{\nu_e}+ \rho_{\bar{\nu}_e}$.
• Figure 3: Parameters for the final $\nu_e$ and $\bar{\nu}_e$ spectra as well as the final $\Delta N_{\rm eff}$ as a function of the initial $\xi_{\nu_e}$. The solid lines correspond to $\theta_{13}=0$, the dotted lines to $\sin^2\theta_{13}=0.04$. In the bottom panel, the dashed line is the surviving $\Delta N_{\rm eff}$ when the final $\xi_{\nu_e}$ is in the range allowed by BBN.