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

TL;DR

This paper derives the most general formula for redshift-dependent in-vacuo dispersion corrections in DSR-relativistic models within FLRW spacetime, highlighting constraints on possible redshift dependencies compared to LIV models.

Contribution

It provides a comprehensive derivation of redshift-dependent time delay corrections in DSR models in curved spacetime, extending previous flat spacetime results and identifying specific allowed redshift dependencies.

Findings

Only linear combinations of three redshift dependence forms are allowed in DSR.

Derived a generalized formula for in-vacuo dispersion in FLRW spacetime.

Identified priority redshift dependencies for quantum-gravity investigations.

Abstract

Studies of in-vacuo dispersion are the most active area of quantum-gravity phenomenology. The way in which in-vacuo dispersion produces redshift-dependent corrections to the time of flight of astrophysics particles depends on the model-dependent interplay between Planck-scale effects and spacetime curvature/expansion, and we here derive the most general formula for the leading order redshift-dependent correction to the time of flight for the scenario in which relativistic symmetries are deformed at the Planck scale (DSR) for the constant-curvature case. We find that, contrary to the broken symmetries scenario (LIV), where in principle any arbitrary form of redshift dependence could be allowed, for the DSR scenario only linear combinations of three possible forms of redshift dependence are allowed. We also derive a generalization of our results to the FRW case, and discuss some specific combinations of the three forms of redshift dependence whose investigation might deserve priority from the quantum-gravity perspective.