Effects of gravitational lensing on neutrino oscillation in Hu-Sawicki f(R) gravity

Gravitational lensing serves as a powerful probe of compact astrophysical objects and dark matter distributions. As relativistic counterparts to photons, neutrinos experiencing lensing offer a complementary means to investigate the properties of curved spacetimes. This paper studies neutrino oscillations within the spacetime geometry described by the Hu-Sawicki f(R) gravity model, focusing on the modifications induced by gravitational lensing. We calculate the oscillation phases for both radial and non-radial neutrino propagation and derive the corresponding flavor transition probabilities for 2-flavor and 3-flavor scenarios under the weak-field approximation. Our analysis demonstrates that the lensing-affected oscillation probabilities exhibit a clear dependence on the Hu-Sawicki model parameter λ, the neutrino mass hierarchy, and the absolute value of the lightest neutrino mass. Furthermore, extending the analysis beyond the weak-field regime reveals that strong-field gravitational lensing amplifies these effects. These results, while theoretical, indicate that future high precision measurements of lensed neutrinos from compact astrophysical objects could, in principle, help test modified gravity models and constrain neutrino parameters, provided that experimental and wave-packet decoherence challenges are overcome.