Time delay of light signals in an energy-dependent spacetime metric

TL;DR

This paper reviews how energy-dependent spacetime metrics, inspired by Gravity-Rainbow and DSR theories, affect photon time delays, showing smaller delays at low redshifts compared to Lorentz invariance violation models.

Contribution

It provides a comparative analysis of time delays in energy-dependent metrics versus Lorentz invariance violation frameworks, highlighting differences at small redshifts.

Findings

Energy-dependent metrics produce smaller time delays at low redshifts.

Corrections are closely related to the DSR proposal.

The approach differs from generic Lorentz invariance violation models.

Abstract

In this note we review the problem of time delay of photons propagating in a spacetime with a metric that explicitly depends on the energy of the particles (Gravity-Rainbow approach). We show that corrections due to this approach -- which is closely related to DSR proposal -- produce for small redshifts ($z<<1$) smaller time delays than in the generic Lorentz Invariance Violating case.