On the Origin of Highest Energy Cosmic Rays
  In this paper we show that the conventional diffusive shock acceleration mechanism for cosmic rays associated with relativistic astrophysical shocks in active galactic nuclei (AGNs) has severe difficulties to explain the highest energy cosmic ray events. We show that protons above around $2\times10^{20}\eV$ could have marginally been produced by this mechanism in an AGN or a rich galaxy cluster not further away than around $100\Mpc$. However, for the highest energy Fly's Eye and Yakutsk events this is inconsistent with the observed arrival directions. Galactic and intergalactic magnetic fields appear unable to alter the direction of such energetic particles by more than a few degrees. We also discuss some other options for these events associated with relativistic particles including pulsar acceleration of high $Z$ nuclei. At the present stage of knowledge the concept of topological defects left over from the early universe as the source for such events appears to be a promising option. Such sources are discussed and possible tests of this hypothesis are proposed. 
G. Sigl, D. N. Schramm and P. Bhattacharjee