# Lorentz Invariance Violation effects on UHECR propagation: a geometrized approach

## TL;DR

This paper investigates how Lorentz Invariance Violation, modeled through Modified Dispersion Relations and Finsler geometry, could explain anomalies in Ultra High Energy Cosmic Ray propagation and the potential modification of the GZK cutoff.

## Contribution

It introduces a geometrized approach to LIV effects on UHECRs, linking quantum space-time structure with observable cosmic ray phenomena, and explores Finsler geometry as a framework.

## Key findings

- LIV via MDRs can modify UHECR propagation predictions.
- Finsler geometry offers a broader space-time structure for LIV theories.
- Potential explanation for GZK cutoff modifications.

## Abstract

We explore the possibility to geometrize the interaction of massive fermions with the quantum structure of space-time, trying to create a theoretical background, in order to explain what some recent experimental results seem to implicate on the propagation of Ultra High Energy Cosmic Rays (UHECR). We will investigate part of the phenomenological implications of this approach on the predicted effect of the UHECR suppression, in fact recent evidences seem to involve the modification of the GZK cut-off phenomenon. The search for an effective theory, which can explain this physical effect, is based on Lorentz Invariance Violation (LIV), which is introduced via Modified Dispersion Relations (MDRs). Furthermore we illustrate that this perspective implies a more general geometry of space-time than the usual Riemannian one, indicating, for example, the opportunity to resort to Finsler theory.