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

Neutrino Lorentz Invariance Violation from Cosmic Fields