Planck-scale dual-curvature lensing and spacetime noncommutativity

TL;DR

This paper investigates Planck-scale dual-curvature lensing caused by momentum-space curvature, demonstrating it is a genuine physical effect rather than a coordinate artifact, with implications for quantum gravity phenomenology.

Contribution

The study provides evidence that dual-curvature lensing is a real phenomenon in $ ho$-Minkowski noncommutative spacetime, independent of dual-curvature redshift effects.

Findings

Dual-curvature lensing is not a coordinate artifact.

It can occur without dual-curvature redshift.

Analysis of $ ho$-Minkowski spacetime supports these conclusions.

Abstract

It was recently realized that Planck-scale momentum-space curvature, which is expected in some approaches to the quantum-gravity problem, can produce dual-curvature lensing, a feature which mainly affects the direction of observation of particles emitted by very distant sources. Several gray areas remain in our understanding of dual-curvature lensing, including the possibility that it might be just a coordinate artifact and the possibility that it might be in some sense a by product of the better studied dual-curvature redshift. We stress that data reported by the IceCube neutrino telescope should motivate a more vigorous effort of investigation of dual-curvature lensing, and we observe that studies of the recently proposed "$\rho$-Minkowski noncommutative spacetime" could be valuable from this perspective. Through a dedicated $\rho$-Minkowski analysis, we show that dual-curvature lensing is not merely a coordinate artifact and that it can be present even in theories without dual-curvature redshift.