Quantum entanglement between neutrino eigenstates in the presence of the subsequent phase shift of the neutrino oscillations

In this study, using von Neumann entropy we examine the entanglement entropy for the neutrino oscillations in the presence of the subsequent phase shift. We numerically show that the entanglement entropy for the subsequent periods of the two-flavor neutrino oscillations increases asymmetrically with time depending on the space-time deformation. We also explored the obtained results for the three-flavor neutrino oscillations to show that this result is also valid for the three-flavor neutrino oscillations. These results, obtained for the first time in this study, are quite different from the computing for the standard neutrino oscillation theory. We concluded that these interesting results play an important role in the cosmology.