Cosmological Lepton Asymmetry, Primordial Nucleosynthesis, and Sterile Neutrinos

TL;DR

The paper analyzes how post-weak-decoupling flavor transformations between active and sterile neutrinos in the early universe—driven by MSW resonances—affect neutrino energy spectra, lepton numbers, and Big Bang Nucleosynthesis. It shows that resonances are generally highly adiabatic but cannot sweep smoothly through the neutrino distribution as the universe expands, producing non-thermal spectra and altering the neutron-to-proton ratio and the He-4 yield. By exploring cases with and without efficient active-active mixing, it demonstrates that sterile neutrinos can reverse or modify the lepton-number effect on BBN, constraining sterile neutrino parameters from cosmological observables such as the closure fraction, CMB, and large-scale structure. The work underscores the potential cosmological tensions for LSND-like sterile neutrinos and highlights how non-thermal spectral distortions must be accounted for in interpreting primordial element abundances and neutrino mass bounds.

Abstract

We study post weak decoupling coherent active-sterile and active-active matter-enhanced neutrino flavor transformation in the early universe. We show that flavor conversion efficiency at Mikheyev-Smirnov-Wolfenstein resonances is likely to be high (adiabatic evolution) for relevant neutrino parameters and energies. However, we point out that these resonances cannot sweep smoothly and continuously with the expansion of the universe. We show how neutrino flavor conversion in this way can leave both the active and sterile neutrinos with non-thermal energy spectra, and how, in turn, these distorted energy spectra can affect the neutron-to-proton ratio, primordial nucleosynthesis, and cosmological mass/closure constraints on sterile neutrinos. We demonstrate that the existence of a light sterile neutrino which mixes with active neutrinos can change fundamentally the relationship between the cosmological lepton numbers and the primordial nucleosynthesis He-4 yield.

Figures (11)

• Figure 1: The nonthermal scaled energy ($E_\nu/T$) distributions $f\left( E_\nu/T\right)$ for $\nu_s$ (dashed) and $\nu_e$ (solid) resulting from smooth, adiabatic resonance sweep from $E_\nu/T = 0$ to $E_\nu/T = \epsilon$.
• Figure 2: The solid line is $\epsilon {\cal{L}}(\epsilon)$, the product of $\epsilon$ and potential lepton number, in the smooth and continuous resonance sweep case for initial lepton numbers $L_{\nu_e}=L_{\nu_\mu}=L_{\nu_\tau}=0.01096$, corresponding to initial potential lepton number ${\cal{L}}(\epsilon=0) = 0.04384$. The arrows give the sense of evolution along this curve as the universe expands and the net potential lepton number decreases as a result of neutrino flavor conversion in the channel $\nu_e\rightarrow \nu_s$ with $\delta m^2\cos2\theta=1\,{\rm eV}^2$. The horizontal dashed lines correspond to values of the right-hand side of Eq. (\ref{['ereseqn']}) for the indicated epochs (temperatures). Solutions to Eq. (\ref{['ereseqn']}) are possible at a given epoch when the corresponding dashed line crosses the $\epsilon {\cal{L}}(\epsilon)$ curve. Physical solutions are circled here for $T=2.0\,{\rm MeV}$ and $1.6\,{\rm MeV}$. The maximum value on the $\epsilon {\cal{L}}(\epsilon)$ curve occurs at $\epsilon_{\rm max}\approx 0.598$, and in the smooth resonance sweep scenario this is reached at $T\approx 1.6\,{\rm MeV}$. Clearly, no solutions are possible in this scenario for $T < 1.6\,{\rm MeV}$. If the system were forced to follow the smooth resonance sweep $\epsilon {\cal{L}}(\epsilon)$ curve beyond $\epsilon_{\rm max}$, the potential lepton number would be completely depleted when $\epsilon$ reaches $\epsilon_{\rm c.o.}\approx 0.987$ ( i.e., ${\cal{L}}(\epsilon_{\rm c.o.})=0)$.
• Figure 3: The values of $\epsilon_{\rm c.o.}$ (solid line) and $\epsilon_{\rm max}$ (dashed line) are shown as functions of total initial potential lepton number in the limit of a smooth and continuous resonance sweep and with the assumption that full active neutrino equilibration obtains ($L_{\nu_e}=L_{\nu_\mu}=L_{\nu_\tau}$).
• Figure 4: Level crossing diagram for the case with lepton numbers as shown and for scaled neutrino energy $\epsilon =1$. The vacuum mass-squared eigenvalue for the (mostly) sterile state is taken as $m^2_4 = 10\,{\rm eV}^2$. This is shown as the dashed curve labeled $\nu_s$. An artificial (exaggerated) $1\,{\rm eV}^2$ offset between the vacuum mass-squared eigenvalues $m_2^2$ and $m_3^2$ has been added so that the curves labeled with $\nu_\mu^\ast$ and $\nu_\tau^\ast$ are separated for clarity. In reality, the top curve should be split from the lower curve by $\delta m^2\approx 3\times{10}^{-3}\,{\rm eV}^2$. Conversion in the channel $\nu_e\rightarrow\nu_s$ is as described in the text.
• Figure 5: Final active neutrino energy distribution function $f_{\nu_\alpha}$ for Cases 1 (short dashed line), 2 (dot dashed line), and 3 (solid line) for the particular case of a continuous resonance sweep scenario and in the instantaneous active-active mixing limit as described in the text. Here $\alpha = {\rm e},\mu,\tau$: all species have the same distribution function. The long dashed line and its continuation as a solid line shows the original thermal distribution function common to all active flavors. The particular scenario shown here has $L_{\nu_e}=L_{\nu_\tau}=L_{\nu_\mu}= 0.1$, so that $\epsilon_1 \approx 3.8$, $\epsilon_2 \approx 2.3$, and $\epsilon_3\approx 1.85$