X-ray and Gamma-ray Polarization Tests of Lorentz Invariance

The Standard Model of particle physics is remarkably successful. But it is known to be incomplete: it does not include gravity, and the nature of dark matter and dark energy are still unknown. The failure of the Large Hadron Collider to detect any new particles except the Higgs boson presents a major challenge to developing our understanding of fundamental physics beyond the Standard Model. On the one hand, the results severely constrain many popular theories of quantum gravity, on the other hand, due the lack of new discoveries there is little guidance for future theoretical developments. Exploring ever higher energy scales in terrestrial laboratories is difficult and will at some point become unfeasible. One possible path forward, is to leverage the vast distance, time, and energy scales of the Universe itself to search for signatures of quantum gravity. Many theories of quantum gravity predict that Lorentz invariance or CPT symmetry may be broken at the Planck energy, and that there may be small residual effects at attainable energies, suppressed by some power of the Planck energy scale. If Lorentz invariance is not a good symmetry of nature, observable effects in the photon sector include vacuum dispersion, birefringence, and anisotropy. Linear polarization of light from distant objects, such as gamma-ray bursts (GRBs) or active galactic nuclei (AGN), enables highly sensitive tests of Lorentz symmetry. Currently, some of the strongest constraints on Lorentz invariance violation (LIV) result from polarization measurements of GRBs and AGN in the optical band. However, due to the energy dependence of expected effects, X-ray and gamma-ray polarization measurements have the potential to explore effects that are 6 -- 12 orders of magnitude smaller than current upper limits. In this paper, I will give a brief overview of the theoretical landscape and introduce the phenomenology of Lorentz invariance violation in the photon sector. I will highlight some recent results, before laying out the potential of upcoming and planned missions such as the Imaging X-ray Polarimetry Explorer (IXPE), the Compton Spectrometer and Imager (COSI), and the All-Sky Medium Energy Gamma-ray Observatory (AMEGO), to further constrain LIV or possibly even discover exciting new physics.