Testing the violations of Lorentz Invariance with accelerator neutrinos in P2O and DUNE

Fundamental symmetry such as the Lorentz Invariance (LI) may spontaneously break at Planck scales in some unified theories. In a low energy effective field theory, such as the Standard Model, Violations of LI (VLI) can manifest itself perturbatively. Such Planck-suppressed VLI signals can affect the mass induced neutrino oscillations at accessible energy ranges and induce spectral changes by modifying both its magnitude and phase. High statistics neutrino experiments represent a potent source of information on neutrino oscillations stemming from its energy and direction dependent multi-layer matter effects. In this contribution, we present the physics reach of long baseline neutrino experiments, namely P2O and DUNE, in measuring sub-dominant effects in neutrino oscillations coming from possible VLI.