Gamma ray burst delay times probe the geometry of momentum space

TL;DR

This paper explores how the geometry of momentum space in the relative locality framework can explain energy-dependent photon delay times and angular deviations from distant gamma ray bursts, linking these effects to non-metricity and torsion.

Contribution

It introduces a novel approach connecting momentum space geometry with observable photon delay and lensing effects, providing new bounds on momentum space tensors.

Findings

Time delays relate to non-metricity of momentum space.

Photon angular deviations are linked to torsion of momentum space.

Experimental bounds constrain the components of momentum space tensors.

Abstract

We study the application of the recently proposed framework of relative locality to the problem of energy dependent delays of arrival times of photons that are produced simultaneously in distant events such as gamma ray bursts. Within this framework, possible modifications of special relativity are coded in the geometry of momentum space. The metric of momentum space codes modifications in the energy momentum relation, while the connection on momentum space describes possible non-linear modifications in the laws of conservation of energy and momentum. In this paper, we study effects of first order in the inverse Planck scale, which are coded in the torsion and non-metricity of momentum space. We find that time delays of order Distance * Energies/m_p are coded in the non-metricity of momentum space. Current experimental bounds on such time delays hence bound the components of this tensor of order 1/m_p. We also find a new effect, whereby photons from distant sources can appear to arrive from angles slightly off the direction to the sources, which we call gravitational lensing. This is found to be coded into the torsion of momentum space.