Several studies have been devoted to the possibility that quantum gravity might tangibly affect relativistic kinematics for particles propagating from distant astrophysical sources to our telescopes, but the relevant literature has so far focused exclusively on a subclass of scenarios such that the quantum-gravity effects are independent of (macroscopic) curvature. It was assumed that a phenomenology for quantum-gravity effects that are triggered by curvature might be a dead end because of a double suppression: by the smallness of the characteristic quantum-gravity length scale and by the smallness of curvature. This state of affairs is becoming increasingly unsatisfactory in light of some recent quantum-gravity studies providing evidence of the fact that the presence of curvature might be required in order to have the novel relativistic properties. We here analyze an explicit scenario for curvature-induced quantum-gravity effects, and show that the smallness of curvature does not pose a challenge for phenomenology since it is compensated by the large distances traveled by the particles considered in the relevant phenomenological studies. We also observe that the present data situation for particles propagating from distant astrophysical sources to our telescopes, while inconclusive, provides more encouragement for our curvature-induced effects than for the curvature-independent effects that were so far studied.
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