  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.
