Light sterile neutrino production in the early universe with dynamical neutrino asymmetries

TL;DR

This work investigates how dynamical lepton asymmetries affect the production of light sterile neutrinos in the early universe, using (3+1) and (2+1) mixing schemes and incorporating CP-violating phases. By solving momentum-averaged quantum kinetic equations with non-linear neutrino self-interactions, it reveals that equal active asymmetries suppress resonant production only when $|L| \sim 10^{-3}$, while opposite asymmetries require $|L| \sim 10^{-2}$, with CP violation potentially enhancing production in some cases. The results imply that even modest asymmetries can leave measurable traces in $N_{\rm eff}$ and the electron-neutrino spectra, affecting BBN through altered freeze-out conditions and helium yields. Overall, sterile neutrinos compatible with laboratory hints are challenging to reconcile with cosmology, and robust predictions require momentum-dependent treatments beyond the averaged-momentum approximation.

Abstract

Light sterile neutrinos mixing with the active ones have been recently proposed to solve different anomalies observed in short-baseline oscillation experiments. These neutrinos can also be produced by oscillations of the active neutrinos in the early universe, leaving possible traces on different cosmological observables. Here we perform an updated study of the neutrino kinetic equations in (3+1) and (2+1) oscillation schemes, dynamically evolving primordial asymmetries of active neutrinos and taking into account for the first time CP-violation effects. In the absence of neutrino asymmetries, eV-mass scale sterile neutrinos would be completely thermalized creating a tension with respect to the CMB, LSS and BBN data. In the past literature, active neutrino asymmetries have been invoked as a way to inhibit the sterile neutrino production via the in-medium suppression of the sterile-active mixing angle. However, neutrino asymmetries also permit a resonant sterile neutrino production. We find that if the active species have equal asymmetries L, a value |L|=10^{-3} is required to start suppressing the resonant sterile production, roughly an order of magnitude larger than what previously expected. When active species have opposite asymmetries the sterile abundance is further enhanced, requiring an even larger |L|\simeq 10^{-2} to start suppressing their production. In the latter case, CP-violation (naturally expected) further exacerbates the phenomenon. Some consequences for cosmological observables are briefly discussed: for example, it is likely that moderate suppressions of the sterile species production are associated with significant spectral distortions of the active neutrino species, with potentially interesting phenomenological consequences especially for BBN.

Figures (10)

• Figure 1: Neutrino collisional and refractive rates (normalized in terms of the Hubble rate) vs. temperature $T$. In particular, we show $\Omega_{\rm vac}$ (solid curve), $\Omega_{\rm matt}$ (long-dotted curve), $\Omega_{\rm asy} \times \Delta_e$ (dashed curve), $\Omega_{\rm sym} \times \Sigma_{ee}$ (short-dotted curve), $\Omega_{\rm coll} \times [(g_s^e)^2 + (g_s^\mu)^2]$ (dash-dotted curve). Here we use $\Delta m^2_{\rm st}$, $\Delta_e= 32 L/3$ with $L=10^{-4}$ and $\Sigma_{ee}=2$ (see the text for more details on these quantities).
• Figure 2: (3+1) scenario. Evolution of the density matrix element $\rho_{ss}$ in function of the temperature $T$. We consider $L=L_e=L_\mu=L_{\tau}$. The solid curve corresponds to $L=0$, the dashed curve to $L=-10^{-4}$, the dotted curve to $L=-10^{-3}$ and the dash-dotted one to $L=-10^{-2}$.
• Figure 3: (3+1) scenario. Evolution of the effective number of degrees of freedom $N_{\rm eff}$ for the cases corresponding to Fig. \ref{['fig2']}
• Figure 4: (2+1) scenario. Evolution in function of the temperature $T$ of $\rho_{ss}$ for different initial neutrino asymmetries. Upper panels correspond to $L=L_e=L_{\mu}$, lower panels correspond to $L=L_e=-L_{\mu}$. The solid curves correspond to $L=0$, the dashed curves to $L=-10^{-4}$, the dotted to $L=-10^{-3}$ and the dash-dotted to $L=-10^{-2}$. Left panels show cases with no CP violation in the sterile neutrino sector, while right panels refers to $\varphi_{\rm CP}=\pi/2$.
• Figure 5: (2+1) case with $L=L_e=L_{\mu}$ and $\varphi_{\rm CP}=0$. Left panels: Evolution $\Delta \rho_{\alpha}= \rho_{\alpha\alpha}- \bar{\rho}_{\alpha\alpha}$ for the $\nu_e$ (solid curve), $\nu_{\mu}$ (dotted curve) and $\nu_s$ (dashed curve) for the different values of initial neutrino asymmetries. Right panels: Evolution of $\Omega_{\rm vac}$ (solid curve) vs $\Omega_{\rm asy}\times \Delta_{e}$ (dashed curve).