Have we already detected astrophysical symptoms of space-time noncommutativity ?

TL;DR

This paper investigates astrophysical effects of space-time noncommutativity in $5$-Minkowski space-time, showing that certain high-energy cosmic phenomena do not exclude such noncommutative models, and derives a velocity formula for particles.

Contribution

It provides a new velocity formula for particles in $5$-Minkowski space-time and analyzes astrophysical reactions related to high-energy cosmic rays and gamma rays.

Findings

Massless particles move at constant speed, consistent with Minkowski space-time.

Arrival time analysis of gamma rays does not exclude space-time noncommutativity.

Reaction processes in $5$-Minkowski space-time relate to high-energy cosmic ray observations.

Abstract

We discuss astrophysical implications of $\kappa$-Minkowski space-time, in which there appears space-time noncommutativity. We first derive a velocity formula for particles based on the motion of a wave packet. The result is that a massless particle moves at a constant speed as in the usual Minkowski space-time, which implies that an arrival time analysis by $\gamma$-rays from Markarian (Mk) 421 does not exclude space-time noncommutativity. Based on this observation, we analyze reaction processes in $\kappa$-Minkowski space-time which are related to the puzzling detections of extremely high-energy cosmic rays above the Greisen-Zatsepin-Kuzmin cutoff and of high-energy ($\sim$20 TeV) $\gamma$-rays from Mk 501.