Gravitationally violated U(1) symmetry and neutrino anomalies

The current searches for neutrino oscillations seem to suggest an approximate Lₑ-L_μ-L_τ flavor symmetry. This symmetry implies a pair of degenerate neutrinos with a mass m₀ and large leptonic mixing. We explore the possibility that gravitational interactions break this global symmetry. The Planck scale suppressed breaking of the Lₑ-L_μ-L_τ symmetry is shown to lead to the right amount of splitting between the degenerate neutrinos needed in order to solve the solar neutrino problem. The common mass m₀ of the pair can be identified with the atmospheric neutrino scale. A concrete model is proposed in which the smallness of m₀ and the hierarchy in the solar and atmospheric neutrino scales get linked to hierarchies in the weak, grand unification, and Planck scales.