Symmetry breaking, and the effect of matter density on neutrino oscillation

A proposal for the neutrino mass, based on neutrino-scalar field interaction, is introduced. The scalar field is also non-minimally coupled to the Ricci scalar and hence relates the neutrino mass to the matter density. In a dense region, the scalar field obeys the $Z_2$ symmetry, and the neutrino is massless. In a dilute region, the $Z_2$ symmetry breaks and neutrino acquires mass from the non-vanishing expectation value of the scalar field. We consider this scenario in the framework of a spherical dense object whose outside is a dilute region. In this background, we study the neutrino flavors oscillation, along with the consequences of the theory on oscillation length and MSW effect. This preliminary model may shed some lights on the existing anomalies within the neutrino data, concerning the different oscillating behavior of the neutrinos in regions with different densities.