(ABRIDGED) The Gamma-ray Large Area Space Telescope (GLAST) will measure the spectra of distant extragalactic sources of high energy gamma-rays. GLAST can look for energy dependent propagation effects from such sources as a signal of Lorentz invariance violation (LIV). Such sources should also exhibit high energy spectral cutoffs from pair production interactions with low energy photons. The properties of such cutoffs can also be used to test LIV. Detectors to measure gamma-ray polarization can look for the depolarizing effect of space-time birefingence predicted by loop quantum gravity. A spaceborne detector array looking down on Earth to study extensive air showers produced by ultrahigh energy cosmic rays can study their spectral properties and look for a possible deviation from the predicted GZK effect as another signal of LIV.
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