Constraining alternative gravity theories using the solar neutrino problem

The neutrino flavor oscillation is studied in some classes of alternative gravity theories in a plane specified by theta = pi/2, exploiting the spherical symmetry and general equations for oscillation phases are given. We first calculate the phase in a general static spherically symmetric model and then we discuss some spherically symmetric solutions in alternative gravity theories. Among them we discuss the effect of a cosmological term in the Schwarzschild-(anti) de Sitter solution, which is the vacuum solution in F(R) theory and the effect of charge and the Gauss-Bonnet coupling parameter on the oscillation phase is presented. Finally, we discuss a charged solution with a spherical symmetry in F(R) theory and also its implication to the oscillation phase. We calculate the oscillation length and transition probability in these spherically symmetric spacetimes and have presented a graphical representation for the transition probability with various choices for parameters in our theory. From this, we have constrained parameters appearing in these alternative theories using standard solar neutrino results.