  The neutrino propagating in curved spacetimes, e.g. around black holes, in
early curved universe, violates Lorentz and then CPT symmetry, at least in the
local coordinate. This occurs due to coupling of spin of the neutrino to
background spin connection which modifies the underlying dispersion relation.
This results in the neutrino asymmetry and hence as a consequence neutrino
oscillation probability gets affected.
