Stringent Constraints on Cosmological Neutrino-Antineutrino Asymmetries from Synchronized Flavor Transformation

TL;DR

This work demonstrates that in the early universe, near bi-maximal neutrino mixing enforces a synchronized MSW-like transformation that rapidly transfers lepton asymmetries from muon and tau flavors into the electron flavor. Using a full two-flavor density-matrix treatment with a dominant neutrino self-potential, the authors show that all momentum modes synchronize to a common effective momentum, causing an adiabatic flavor evolution that closely matches the average-momentum case. Consequently, stringent bounds on the electron-neutrino degeneracy translate into strong limits on initial muon/tau asymmetries, e.g., $|\xi_e^f| \lesssim 0.04$ and $|\xi_\mu^i+\xi_\tau^i| \lesssim 0.5$, with corresponding $\Delta N_\nu$ implications. These results reinforce how cosmological observations and neutrino-mixing phenomenology jointly constrain the net lepton number of the universe and will be sharpened by forthcoming precision CMB and neutrino-oscillation experiments.

Abstract

We assess a mechanism which can transform neutrino-antineutrino asymmetries between flavors in the early universe, and confirm that such transformation is unavoidable in the near bi-maximal framework emerging for the neutrino mixing matrix. We show that the process is a standard Mikheyev-Smirnov-Wolfenstein flavor transformation dictated by a synchronization of momentum states. We also show that flavor ``equilibration'' is a special feature of maximal mixing, and carefully examine new constraints placed on neutrino asymmetries. In particular, the big bang nucleosynthesis limit on electron neutrino degeneracy xi_e < 0.04 does not apply directly to all flavors, yet confirmation of the large-mixing-angle solution to the solar neutrino problem will eliminate the possibility of degenerate big bang nucleosynthesis.

Figures (6)

• Figure 1: Vector precession diagram. The angles and magnitudes of the vectors are not to scale but have been exaggerated for clarity. For the situation of interest, the magnitude of ${\mathbf I}$ is much greater than that of ${\mathbf A}_{\rm eff}$. When this condition holds, it is a good approximation to describe the evolution of the polarization vectors for the individual momentum modes ${\mathbf P}_p$ as a precessing about ${\mathbf I}$. The vector ${\mathbf I}$ then precesses about ${\mathbf A}_{\rm eff}$, in the manner of a single momentum mode in the absence of the self-term. For asymmetries between neutrino flavors in the early universe, ${\mathbf A}_{\rm eff}$ and ${\mathbf I}$ are both initially aligned with the $z$ axis, and, for maximal mixing, both adiabatically evolve to align with the $x$ axis.
• Figure 2: The angle between ${\mathbf A}_p$ and the $z$ axis is shown in the upper panel, in color, as a function of the temperature of the universe (horizontally) and across the neutrino spectrum (vertically). In the lower panel, the angle between ${\mathbf P}_p$ and the $z$ axis is displayed in the same fashion. As detailed in the text, all ${\mathbf P}_p$ ignore the momentum dependence of ${\mathbf A}_p$ and are dramatically synchronized to a single effective momentum, $p_{sync}/T \simeq \pi$. That is, all of the ${\mathbf P}_p$ follow the orientation (i.e., have the same color) of ${\mathbf A}_p$ at $p/T \simeq \pi$, shown with a white horizontal dashed line.
• Figure 3: We show the angle between individual ${\mathbf P}_p$ and ${\mathbf I}$ as a function of temperature of the universe (horizontally) and the neutrino spectrum (vertically). The angles are extremely small, indicating the degree of synchronization.
• Figure 4: The evolution of $J_i$ in the synchronized case with LMA parameters. As described in the text, the behavior is essentially a MSW transformation $\nu_e\leftrightarrow\nu^\ast_\mu$. The antineutrinos $|\bar{J}_i|$ evolve identically. The fact that $J_y$ is never large demonstrates that all of the precession angles are small enough that the evolution is dominantly in the $x-z$ plane. The evolution of $P_i$ and $\bar{P}_i$ at the average momentum is the same if one excludes the self-potentials in Eq. (\ref{['veceqns']}).
• Figure 5: The evolution of $J_i$ ($\bar{J}_i$ are identical) for the mu and tau neutrino transformation with and without the inclusion of thermal $\mu^\pm$ pairs. The spiky features indicate real oscillations going through zero, and the depth of the spikes on the logarithmic scale is an artifact of numerical sampling. Those oscillations are real and are determined by the atmospheric $\delta m^2_0$. In the lower panel, $J_x$ is zero since the mixing angle is maximal. Collisions have been ignored.