arXiv highlights

Sterile neutrinos remain a well-motivated dark-matter candidate whose cosmological abundance can be enhanced by resonant active--sterile conversion in the presence of a lepton asymmetry in primordial plasma. In the standard picture, a larger initial asymmetry increases the matter potential and can therefore promote resonant production. However, the same increase also shifts the resonance to later stages of the cosmological evolution when the plasma temperature is lower. We show that this delayed production epoch can overlap with the onset of active neutrino oscillations, which redistribute the flavor asymmetries and may substantially reduce, or in some cases nearly erase, the lepton asymmetry needed for a successful resonant sterile-neutrino production. This interplay provides a natural saturation mechanism for the final sterile-neutrino abundance: beyond a certain range of initial asymmetries, increasing the primordial asymmetry no longer leads to a proportional increase in the produced dark-matter density. We identify this effect as an additional constraint on resonant sterile-neutrino production at large lepton asymmetry and discuss its dependence on the flavor structure of the initial asymmetry and on the background cosmological evolution. Our numerical results reveal two order of magnitude range in sterile-active neutrino mixing parameter $\sin^2(2\theta)$ presently consistent with the resonant mechanism of the dark matter sterile neutrino production. It must be investigated by the next generation X-ray telescopes to fully explore this mechanism and corresponding minimal models suggesting sterile neutrinos as viable dark matter. We also consider pion condensation at large flavor lepton asymmetries, which may lead to a first-order QCD phase transition and associated gravitational-wave production in the early Universe.

This Letter transitions neutrino mixing from an empirical fit to a geometric law by analytically deriving the PMNS mixing angles and mass spectrum from an $A_5$ topological manifold. Solving the Quantum Yang-Baxter Equation forces a geometric fracture at $M_0 \approx 3.88 \times 10^{16}$ GeV. Projecting this to the Electroweak scale yields parameter-free targets: maximal CP violation $\delta_{CP} = \pm \pi/2$, a mass sum $\sum m_i \approx 72.48$ meV, with $m_1 < m_3$, and effective masses $m_\beta \approx 12.47$ meV and $m_{\beta\beta} \approx 8.20$ meV, setting definitive experimental thresholds.

We present the implementation of a multidimensional general-relativistic Boltzmann solver for neutrino transport using the finite volume method. We extend the general-relativistic magnetohydrodynamics solver \texttt{Gmunu} to discretize the full $6$D phase space. We discretize the momentum space in spherical coordinates in the comoving frame, and the position space in the lab frame in Cartesian, cylindrical or spherical coordinates. As in the M1 scheme, we expand the interaction kernels up to first order in a Legendre series. We present a discretization scheme that ensures consistency between the number-conservative and non-conservative formulations in empty flat spacetime, multiple dimensions and coordinate systems, conserves energy to $\sim 1\%$ with $20$ energy bins in 1D tests. We discuss optimizations of the implicit solver for stiff source terms to minimize its computational cost. In particular, we introduce a method that leverages the Legendre expansion of the kernels to reduce the dimensionality of the problem. In a 1D core-collapse supernova snapshot, our method yields a speed-up factor of $300$ compared to a full-matrix LU method for $14$ angular bins when including energy- and species-coupling interactions. Finally, we validate our implementation on standard test cases and report quadratic convergence in space, energy and propagation angles. We compare our solver to the M1 scheme in simplified 1D configurations and find differences of about $10\%$ in the free-streaming luminosities in relaxation test cases, which we attribute primarily to the M1 closure relation. The average energies, on the other hand, agree between the two methods. We compare both methods on a core-collapse supernova test case and find an overall good agreement in the fluid variables' profiles at the time of core bounce for $20$ energy bins.