High Energy Cosmic Neutrinos and the Equivalence Principle
  Observation of the 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 effects of violation of the equivalence principle (VEP) on propagation of these cosmic neutrinos. Two effects are studied: (1) the oscillations of neutrinos due to the VEP in the gravitational field of our Galaxy and in the intergalactic space, (2) the resonance flavor conversion driven by the gravitational potential of the AGN. We show that the ultra-high energies of the neutrinos as well as cosmological distances to the AGN, or strong AGN gravitational potential will allow one to improve the accuracy of test of the equivalence principle by 21 orders of magnitude for massless or degenerate neutrinos ($\Delta f \sim 10^{-41}$) and at least by 12 orders of magnitude for massive neutrinos ($\Delta f \sim 10^{-28} \times (\Delta m^2/1 {\rm eV}^2)$). Experimental signatures of the transitions induced by the VEP are discussed. 
Hisakazu Minakata and Alexei Yu. Smirnov