Redshift and lateshift from homogeneous and isotropic modified dispersion relations

TL;DR

This paper investigates how modified dispersion relations, possibly from quantum gravity, affect cosmological redshift and lateshift phenomena, deriving generalized formulas and analyzing observational implications.

Contribution

It derives the most general first-order perturbation formulas for redshift and lateshift in homogeneous and isotropic spacetimes, extending previous models.

Findings

Modified dispersion relations can cause both, one, or none of the effects to first order.

The formulas generalize existing results in the literature.

Observational data from gamma ray bursts are used to analyze these effects.

Abstract

Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the later is currently analyzed on the basis of the available observational data from gamma ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homogeneous and isotropic spacetimes and derive the red- and lateshift to first order in the perturbation. Our result generalizes the existing formulae in the literature and we find that there exist modified dispersion relations causing both, one or none of the two effects to first order.