Spontaneous Violation of Lorentz Invariance and Ultra-High Energy Cosmic   Rays
  We propose that local Lorentz invariance is spontaneously violated at high energies, due to a nonvanishing vacuum expectation value of a vector field \phi^\mu, as a possible explanation of the observation of ultra-high energy cosmic rays with an energy above the GZK cutoff. Certain consequences of spontaneous breaking of Lorentz invariance in cosmology are discussed. 
J. W. Moffat