# The optical depth including Lorentz invariance violation energy threshold shifts

## TL;DR

This paper reviews how Lorentz invariance violation affects photon pair-production thresholds, explores its impact on gamma-ray flux, and sets limits on LIV energy scales using TeV gamma-ray spectra, also predicting GZK-photon fluxes.

## Contribution

It provides a comprehensive review of LIV effects on optical depth, derives new constraints on LIV energy scales, and predicts GZK-photon fluxes considering LIV modifications.

## Key findings

- Stringent limits on LIV energy scale at n=1 and 2
- Modified gamma-ray flux predictions due to LIV
- Constraints from TeV gamma-ray spectra

## Abstract

Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations can change the photon energy threshold of pair-production, which modifies the expected gamma-ray flux from astrophysical sources. In this work, we review this phenomenon and explore its consequences through the derived effects in the optical depth. Then, by looking for subluminal LIV signatures in TeV gamma-ray spectra, we present stringent limits to the LIV energy scale at leading order n=1 and 2. And finally, we present the predicted flux of GZK-photons including LIV, in the astrophysical scenario which best describes UHECR data.