Density matrix components averaged throughout the neutron star merger simulation box. It is possible to identify three phases in the evolution of the neutrino flavor. Linear growth phase (yellow shaded area): Unstable coherent flavor oscillation modes cause the off-diagonal components of the density matrices to grow exponentially. Saturation phase (before the linear growth phase): Flavor oscillation modes that started the simulation with small amplitudes grow, creating a combination of high amplitude modes. Decoherence phase (late times in the figure): The flavor oscillation modes start evolving independently at different phases, creating a complex nonlinear flavor oscillation phenomenon. The domain-averaged density matrix finally reaches an asymptotic state close to flavor equilibrium.

Impact of the exponential divergence between the flavor states of two neutron star merger simulation boxes (baseline and perturbed) with close initial conditions on a single computational particle in the EMU code. The electron, muon and tau panels show the behavior of the diagonal components of the density matrix for a single computational particle in the baseline (blue dotted lines) and the perturbed simulations (orange dotted lines). The difference between the components of the density matrix  is shown as solid black lines. Although the components of the density matrix of both simulations evolve close to each other for the first 65 ns, the exponential divergence rapidly separates both simulations, making them evolve independently. The maximum values of difference of the density matrix components of both are comparable to the density matrix components. The lower panel shows the behavior of the trace of the difference between the density matrix components. A clear exponential trend drives the dynamics of the trace of the difference between the density matrix components until it finally reaches the maximum possible value of one (black dotted line) as the the trace ofthe density matrix components is one.

CMB spectral distortions constrain on PBH mass and PBH - dark matter density fraction. The gray region shows forbidden values of the PBH masses and PBH - dark matter density fraction due to the experimental limit set by the cosmic microwave background data obtained by the COBE-FIRAS satellite.

Constraints on PBH mass and PBH - dark matter density fraction due to the CMB spectral distortions of type mu (top) and y (below). The region above the blue and black line is forbidden by the COBE-FIRAS data. The prohibited sample values are represented by +.