Abstract
While it is known that our current theories of quantum interactions and gravitation cannot describe the Planck scale, the effective scale at which the unification of forces into a quantum theory of gravity occurs is yet unknown. The attempts to build new theories are recently being complemented by an intense program aiming at deriving a phenomenology that could be probed by current or future observations. Several proposals, including brane/extra dimensional theories, alternative theories of gravitation such as Horava-Lifshitz theory and emergent theories, have been found to possibly provide low-energy signatures that could be probed with astrophysical messengers as described in Addazi et al. (2022). The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterised by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers from numerous origins. Photons, neutrinos, cosmic rays and gravitational waves give us information about their sources in the universe and the properties of the intergalactic medium, but also opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. Notably, several models imply that a unified theory could break fundamental symmetries such as CPT or Lorentz invariance. Such a break from core assumptions of our theories leads to specific predictions that can be observed with gravitational radiation, electromagnetic signals and neutrino oscillations. This talk will cover the current experimental bounds on those phenomena as well as the progress that can be expected in the next few years.