Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency

TL;DR

This paper investigates how modifications to relativistic kinematics at high energies affect electron-positron production thresholds, finding that certain deformations compatible with relativity could explain cosmic gamma-ray observations.

Contribution

It derives threshold energy equations for photon-photon interactions under deformed kinematics, including energy-momentum conservation modifications, compatible with relativity.

Findings

A few TeV scale deformation is compatible with cosmic gamma-ray data.

Threshold energy equations are derived to first order in inverse high-energy scale.

Relativistic deformations can explain universe transparency without Lorentz violation.

Abstract

We analyze the kinematics of electron-positron production in a photon-photon interaction when one has a modification of the special relativistic kinematics as a power expansion in the inverse of a new high-energy scale. We derive the equation for the threshold energy of this reaction to first order in this expansion, including the effects due to a modification of the energy-momentum conservation equation. In contrast with the Lorentz invariance violation case, a scale of the order of a few TeV is found to be compatible with the observations of very high-energy cosmic gamma rays in the case of a modification compatible with the relativity principle.