  Observations of gamma-ray bursts are being used to test for a momentum
dependence of the speed of photons, partly motivated by preliminary results
reported in analyses of some quantum-spacetime scenarios. The relationship
between time of arrival, momentum of the photon and redshift of the source
which is used for these purposes assumes a "breakdown" of relativistic
symmetries, meaning that it is a preferred-frame scenario which does not
satisfy the Relativity Principle. The alternative hypothesis of a "deformation"
of relativistic symmetries, which preserves the Relativity Principle by
adopting deformed laws of relativistic transformation between observers, could
not so far be tested in gamma-ray-burst observations because it was not known
how to formulate it in expanding spacetimes. We here provide such a
formulation, and we find that also for the symmetry-deformation scenario the
analysis of gamma-ray-burst data take us very close to the desired
"Planck-scale sensitivity".
