Investigation of equivalence principle violations using solar neutrino oscillations in a constant gravitational potential

Neutrino oscillations induced by a flavor-dependent violation of the Einstein equivalence principle (VEP) have been recently considered as a suitable explanation of the solar ${\ensuremath{\nu}}_{e}$ deficiency. Unlike the MSW oscillation mechanism, the VEP mechanism is dependent on a coupling to the local background gravitational potential $\ensuremath{\Phi}$. We investigate the differences which arise by considering three-flavor VEP neutrinos oscillating against fixed background potentials and against the radially dependent solar potential. This can help determine the sensitivity of the gravitationally induced oscillations to both constancy and size (order of magnitude) of $\ensuremath{\Phi}$. In particular, we consider the potential of the local supercluster, $|{\ensuremath{\varphi}}_{\mathrm{SC}}|=3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, in light of recent work suggesting that the varying solar potential has no effect on the oscillations. The possibility for arbitrarily large background potentials in different cosmologies is discussed, and the effects of one such potential $(\ensuremath{\Phi}{=10}^{\ensuremath{-}3})$ are considered.