  A vector field is assumed to be conformally coupled to the matter components
through a screening mechanism. The matter density implicitly affects the
neutrino flavor transitions through the vector field. We study the
neutrino-vector field interaction in the presence of a finite-size matter
density like the Sun and compute the discrepancy in the total flux of solar
electron-neutrinos. Considering existing neutrino flavor conversion data, we
find that for the non-standard vector-neutrino interactions, significant matter
effects might be possible.
