  X-ray and gamma-ray observations of astrophysical objects at cosmological
distances can be used to probe the energy dependence of the speed of light with
high accuracy and to search for violations of Lorentz invariance and CPT
symmetry at the Planck energy scale. In this conference contribution, we
discuss these searches in the theoretical framework of the Standard-Model
Extension. We present new limits on the dispersion relation governed by
operators of mass dimension d=5 and d=6, and we discuss avenues for future
progress.
