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Studies of in-vacuo dispersion are the most active area of quantum-gravityphenomenology. The way in which in-vacuo dispersion produces redshift-dependentcorrections to the time of flight of astrophysics particles depends on themodel-dependent interplay between Planck-scale effects and spacetimecurvature/expansion, and we here derive the most general formula for theleading order redshift-dependent correction to the time of flight for thescenario in which relativistic symmetries are deformed at the Planck scale(DSR) for the constant-curvature case. We find that, contrary to the brokensymmetries scenario (LIV), where in principle any arbitrary form of redshiftdependence could be allowed, for the DSR scenario only linear combinations ofthree possible forms of redshift dependence are allowed. We also derive ageneralization of our results to the FRW case, and discuss some specificcombinations of the three forms of redshift dependence whose investigationmight deserve priority from the quantum-gravity perspective.

Phenomenology of DSR-relativistic in-vacuo dispersion in FLRW spacetime