Probing modified dispersion relations in vacuum with high-energy γ-ray sources: review and prospects

A possible violation of Lorentz Invariance (LIV) in the form of Modified Dispersion Relations (MDR) for photons in vacuum appeared in the late 90s as a possible outcome of some models developed with the goal to provide a full theory of Quantum Gravity (QG). Since then, several ways to probe quantum spacetime from high-energy gamma-ray observations of distant sources have been followed and provide stringent limits on the characteristic energy scale of these QG-related phenomena. In this paper, the use of astrophysical sources for constraining MDR will be described. In particular, strengths and weaknesses of each category of sources as well as temporal effects due to emission mechanisms will be discussed. The latest results obtained from observations of Gamma-Ray Bursts, flaring Active Galactic Nuclei and pulsars will be briefly reviewed. Then, efforts on-going to get more robust constraints on MDR and LIV will be discussed and put in context with the beginning of the Cherenkov Telescope Array operations in the next few years.