Testing the effective scale of quantum gravity with the next generation of gamma ray telescopes

The actual potential of the next generation of gamma ray telescopes in improving the existing tests of an effective quantum gravity scale from the study of the propagation delay for gamma rays of different energies coming from a distant astrophysical source is discussed. It is shown that the existence of a cosmological gamma ray horizon, will impose very demanding conditions on the observations of the telescopes to try to test a quantum gravity scale close to the Planck mass.