  We construct the theta-exact covariant noncommutative (NC) model and obtain
various closed constraints on the NC scale (Lambda_NC) from inelastic
neutrino-nucleon scatterings (nu N -> nu+X), from plasmon decay into neutrino
pair (gamma_pl -> bar nu + nu), from the BBN nucleosynthesis and from the
reheating phase after inflation, respectively. We have have found neutrino
two-point function in a closed form. It shows decoupling of the UV divergent
term from softened UV/IR mixing term and from the finite terms as well. We show
that problematic UV divergent and UV/IR mixing terms vanish for a certain
choice of the noncommutative parameter theta which preserves unitarity. We find
non-perturbative modifications of the neutrino dispersion relations which are
assymptotically independent of the scale of noncommutativity in both the low
and high energy limits and may allow superluminal propagation.
