High energy neutrino oscillation at the presence of the Lorentz Invariance Violation

Due to quantum gravity fluctuations at the Planck scale, the space-time manifold is no longer continuous, but discretized. As a result the Lorentz symmetry is broken at very high energies. In this article, we study the neutrino oscillation pattern due to the Lorentz Invariance Violation (LIV), and compare it with the normal neutrino oscillation pattern due to neutrino masses. We find that at very high energies, neutrino oscillation pattern is very different from the normal one. This could provide an possibility to study the Lorentz Invariance Violation by measuring the oscillation pattern of very high energy neutrinos from a cosmological distance.