We report the results found in Phys. Lett. B 820 (2021) 136595, where we explore the phenomenological viability of scenarios, suggested by different approaches to quantum spacetime, in which quantum-gravity effects in the propagation of particles are triggered by spacetime curvature/expansion.
We rely on a toy model of curvature-induced Lorentz violation for a preliminary exploration, and we find that, differently from what commonly believed, the double suppression due to Planck-length and spacetime curvature is compensated by the high energies and the long (cosmological) distances traveled of the gamma-ray-burst photons.