Weak doubly special relativity and ultra-high energy cosmic ray   experiments
  Should projects of space experiments on ultra-high energy cosmic rays be supported, whatever AUGER results will turn out to be? We claim that this is indeed the case. It is now widely admitted that models of Lorentz symmetry violation (LSV) at the Planck scale based on power-like extrapolations down to cosmic-ray scales and able to account for a possible absence of the Greisen-Zatsepin-Kuzmin cutoff exist and require the existence of a privileged inertial rest frame, as we proposed in 1997 (paper physics/9704017 and subsequent work). The favoured energy dependence of the LSV parameter will then be quadratic rather than linear. This approach (weak doubly special relativity, WDSR) is different from the version of doubly special relativity defended by several authors, where the laws of Physics are required to be exactly identical in all inertial reference frames (strong doubly special relativity, SDSR). To date, WDSR patterns based on a deformation of special relativity with a privileged (vacuum) rest frame are the only clear and consistent candidate to explain a possible absence of the GZK cutoff invoking deviations from standard relativity. It is also to be emphasized, as in hep-ph/0510361, that the usual hypothesis of a power-like dependence of the LSV effective parameters not being altered by any intermediate energy scale is not the only possible one. Therefore, experiments sensitive to UHCR energies as high as possible become necessary irrespective of AUGER results. 
Luis Gonzalez-Mestres (LAPP Annecy-le-Vieux, CNRS-IN2P3, France, UMR   5814)