Neutrino asymmetry in presence of gravitational interaction

Propagation of fermions in curved space-time generates a gravitational interaction due to the coupling between spin of the fermion and space-time curvature. This gravitational interaction, which is an axial-vector appears as the CPT violating term in the Lagrangian, can generate the neutrino asymmetry in Universe. If the back-ground metric is spherically asymmetric, say, of rotating black hole, the axisymmetric space-time of an expanding Universe, this interaction as well as the neutrino asymmetry is non-zero.