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 θ = π/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. (paper)