Cosmological lepton asymmetry with a nonzero mixing angle θ_{13}

TL;DR

This work investigates cosmological constraints on relic neutrino lepton asymmetries, incorporating flavor oscillations and two representative values of the mixing angle $\sin^2\theta_{13}$. Using a detailed treatment of neutrino distribution functions and their impact on $N_{\rm eff}$ and $Y_p$, the authors show that larger $\theta_{13}$ drives faster flavor equilibration, tightening bounds on the total asymmetry and maintaining BBN as the dominant constraint for current data. They also assess the robustness of these limits against additional datasets and perform a forecast for the COrE mission, finding potential improvements of up to a factor of 6.6 in leptonic asymmetry limits and competitive constraints on the neutrino mass sum, illustrating the role of future CMB measurements in probing early-Universe neutrino physics. The results emphasize that, while CMB observations can substantially improve limits, BBN remains essential for determining the sign of the asymmetries, and any significant excess in $N_{\rm eff}$ would point to new physics such as sterile neutrinos.

Abstract

While the baryon asymmetry of the Universe is nowadays well measured by cosmological observations, the bounds on the lepton asymmetry in the form of neutrinos are still significantly weaker. We place limits on the relic neutrino asymmetries using some of the latest cosmological data, taking into account the effect of flavor oscillations. We present our results for two different values of the neutrino mixing angle θ_{13}, and show that for large θ_{13} the limits on the total neutrino asymmetry become more stringent, diluting even large initial flavor asymmetries. In particular, we find that the present bounds are still dominated by the limits coming from Big Bang Nucleosynthesis, while the limits on the total neutrino mass from cosmological data are essentially independent of θ_{13}. Finally, we perform a forecast for COrE, taken as an example of a future CMB experiment, and find that it could improve the limits on the total lepton asymmetry approximately by up to a factor 6.6.

Figures (7)

• Figure 1: Final contribution of neutrinos with primordial asymmetries to the radiation energy density. The isocontours of $N_{\mathrm{eff}}$ on the plane $\eta_{\nu_e}^{\mathrm{in}}$ vs. $\eta_{\nu}$, including flavor oscillations, are shown for two values of $\sin^2\theta_{13}$: $0$ (blue solid curves, left panel) and $0.04$ (red solid curves, right panel) and compared to the case with zero mixing (dashed curves). The dotted line corresponds to $\eta_{\nu}=\eta_{\nu_x}$ ($x = \mu, \tau$), where one expects oscillations to have negligible effects.
• Figure 2: One-dimensional posterior probability density for $m_1$, $\eta_{\nu_e}^{\mathrm{in}}$, and $\eta_{\nu}$ for the WMAP+He dataset.
• Figure 3: 68% and 95% confidence regions in total neutrino asymmetry $\eta_{\nu}$ vs. the primordial abundance of Helium $Y_p$ plane for $\theta_{13}=0$ (blue) and $\sin^2\theta_{13}=0.04$ (red), from the analysis of the WMAP+He dataset. Notice the much stronger constraint for the nonzero mixing angle due to the faster equilibration of flavor asymmetries.
• Figure 4: Two-dimensional 68% and 95% confidence regions in the $(\eta_\nu,\,N_\mathrm{eff}$) plane from the analysis of the WMAP+He dataset, for $\theta_{13}=0$ (blue) and $\sin^2\theta_{13}=0.04$ (red). Even for zero $\theta_{13}$ the data seem to favor $N_{\mathrm{eff}}$ around the standard value $N_{\mathrm{eff}}=3.046$.
• Figure 5: One-dimensional posterior probability density for $\eta_{\nu}$ comparing the WMAP+He and the ALL datasets. As mentioned in the text, the constraints on the total asymmetry do not improve significantly with the inclusion of other cosmological datasets, as they are mainly driven by the determination of the primordial Helium abundance.