Gravitational coupling of neutrinos to matter vorticity: Microscopic asymmetries

We examine the gravitational coupling of neutrinos to matter vorticity; in the context of the Einstein theory of gravitation and for technical simplicity, we have considered the Gödel model as the cosmological background, whose matter content has a non-null vorticity. The presence of a vorticity field of matter generates, via gravitation, microscopic asymmetries in neutrino physics. At the microscopic level, currents are asymmetric along the direction determined by the vorticity field: Neutrino (antineutrino) currents are larger along the direction antiparallel (parallel) to the vorticity field. In the case of production of pairs under $\mathrm{CP}$ violation, a net number asymmetry is generated between neutrinos and antineutrinos.