  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.
