Can the Sun shed light on neutrino gravitational interactions?

We have examined the effects of a large gravitational field on the phenomenon of neutrino oscillations as contemplated in the Mikheyev-Smirnov-Wolfenstein mechanism. We find that the Sun's gravitational field would amplify any small breakdown in the universality of the gravitational coupling by many orders of magnitude. A breakdown of only 1 part in 10¹⁴ would still make the gravitational effect comparable to the conventional weak interaction. The differing energy dependences of the two level-crossing mechanisms can therefore be used as a very sensitive tool to test the conventional universality hypothesis.