Effects of spacetime geometry on neutrino oscillation inside a core-collapse supernova

Neutrinos are excellent probes of the inner structures of supernovas. However, an understanding of their dynamics remains incomplete, which is crucial for properly interpreting the detector data. The huge matter density inside a core collapse supernova affects the self-coupling of the neutrinos through a geometrical four-fermion interaction induced by spacetime torsion generated by the fermions themselves. For normal mass hierarchy, the effect is negligible; for inverted mass hierarchy however, we find that the gravitational coupling can significantly alter the flavor dynamics. The possibility of constraining the said interactions through the relative abundance of different flavors of the neutrinos is discussed.