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We construct the theta-exact covariant noncommutative (NC) model and obtainvarious closed constraints on the NC scale (Lambda_NC) from inelasticneutrino-nucleon scatterings (nu N -> nu+X), from plasmon decay into neutrinopair (gamma_pl -> bar nu + nu), from the BBN nucleosynthesis and from thereheating phase after inflation, respectively. We have have found neutrinotwo-point function in a closed form. It shows decoupling of the UV divergentterm from softened UV/IR mixing term and from the finite terms as well. We showthat problematic UV divergent and UV/IR mixing terms vanish for a certainchoice of the noncommutative parameter theta which preserves unitarity. We findnon-perturbative modifications of the neutrino dispersion relations which areassymptotically independent of the scale of noncommutativity in both the lowand high energy limits and may allow superluminal propagation.

Photon-neutrino interaction in theta-exact covariant noncommutative model: Phenomenology and Quantum properties*