Space-Time Foam and Cosmic-Ray Interactions

It has been proposed that propagation of cosmic rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (``foam''). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of spacetime foam. The strength of the foam is characterized by the factor (E/M_P)^a, where ``a'' is a phenomenological suppression parameter. We find that there exists a critical value of ``a'' (dependent on the particular reaction), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. We also find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10^8 TeV on the context of this model for the scale of gravity. Finally, we comment in the apparent non-conservation of particle energy-momentum, and speculate on its re-emergence as dark energy in the foamy vacuum.