Testing the Principle of Equivalence by Solar Neutrinos

We discuss the possibility of testing the principle of equivalence with solar neutrinos. If there exists a violation of the equivalence principle quarks and leptons with different flavors may not universally couple with gravity. The method we discuss employs a quantum mechanical phenomenon of neutrino oscillation to probe into the non-universality of the gravitational couplings of neutrinos. We develop an appropriate formalism to deal with neutrino propagation under the weak gravitational fields of the sun in the presence of the flavor mixing. We point out that solar neutrino observation by the next generation water Cherenkov detectors can improve the existing bound on violation of the equivalence principle by 3-4 orders of magnitude if the nonadiabatic Mikheyev-Smirnov-Wolfenstein mechanism is the solution to the solar neutrino problem.