  The interest of part of the quantum-gravity community in the possibility of
Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for
testing the relevant scenarios with analyses, from a signal-propagation
perspective, of observations of bursts of particles from cosmological
distances. In this respect the fact that so far the implications of deformed
Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes
represents a very significant limitation, since for propagation over
cosmological distances the curvature/expansion of spacetime is evidently
tangible. We here provide a significant step toward filling this gap by
exhibiting an explicit example of Planck-scale-deformed relativistic symmetries
of a spacetime with constant rate of expansion (deSitterian). Technically we
obtain the first ever example of a relativistic theory of worldlines of
particles with 3 nontrivial relativistic invariants: a large speed scale
("speed-of-light scale"), a large distance scale (inverse of the
"expansion-rate scale"), and a large momentum scale ("Planck scale"). We
address some of the challenges that had obstructed success for previous
attempts by exploiting the recent understanding of the connection between
deformed Lorentz symmetry and relativity of spacetime locality. We also offer a
preliminary analysis of the differences between the scenario we here propose
and the most studied scenario for broken (rather than deformed) Lorentz
symmetry in expanding spacetimes.
