High Energy Cosmic Neutrinos and the Equivalence Principle

Observation of ultra-high energy neutrinos, in particular detection of $\nu_{\tau}$, from cosmologically distant sources like active galactic nuclei (AGN) opens new possibilities to search for neutrino flavor conversion. We consider the effects of violation of the equivalence principle (VEP) on propagation of these cosmic neutrinos. In particular, we discuss the two effects: (1) the oscillations of neutrinos due to VEP in the gravitational field of our Galaxy and in the intergalactic space, (2) resonance flavor conversion driven by the gravitational potential of AGN. We show that ultra-high energies of the neutrinos as well as cosmological distances to AGN, or strong AGN gravitational potential allow to improve the accuracy of testing of the equivalence principle by 25 orders of magnitude for massless neutrinos ($\Delta f \sim 10^{-41}$) and by 11 orders of magnitude for massive neutrinos ($\Delta f \sim 10^{-28} \times (\Delta m^2/1 {\rm eV}^2)$). The experimental signatures of the transitions induced by VEP are discussed.