Neutrino Lorentz Invariance Violation from Cosmic Fields

From a cosmological perspective, scalar fields are well-motivated dark matter and dark energy candidates. Several possibilities of neutrino couplings with a time-varying cosmic field have been investigated in the literature. In this work, we present a framework in which violations of Lorentz invariance (LIV) and $CPT$ symmetry in the neutrino sector could arise from an interaction among neutrinos with a time-varying scalar field. Furthermore, some cosmological and phenomenological aspects and constraints concerning this type of interaction are discussed. Potential violations of Lorentz and $CPT$ symmetries at present and future neutrino oscillation experiments such as IceCube and KM3NeT can probe this scenario.