Exploring Lorentz Violation in Spacetime through Universal Finsler Geometry

TL;DR

The paper addresses LV in spacetime by proposing that a single universal Finsler geometry underlies all LV effects, rather than particle-specific Finsler structures. It derives MDRs from a leading-order Finsler norm and shows that a universal norm with sign $A$ implies either subluminal or superluminal LV across all massive particles. The authors identify three mass-proportional LV scales, ${E_{ m LV,I}}$, ${E_{ m LV,E}}$, and ${E_{ m LV,C}}$, and connect these to time delays, high-energy MDR behavior, and the breakdown of simple expansions, comparing predictions with photon, neutrino, and electron constraints to estimate $A\simeq -10^{-28}$. The work offers a geometric unification of LV in a cosmological context and proposes specific, testable implications for astroparticle phenomenology, while noting the current framework cannot directly treat massless LV and inviting further investigation.

Abstract

Finsler geometry serves as a fundamental and natural extension of Riemannian geometry, providing a valuable framework for investigating Lorentz violation in spacetime. Previous studies have treated the Finsler structures associated with different particles as distinct entities. In this paper, we propose a novel hypothesis suggesting that the Finsler structure may represent an intrinsic property of the universe itself. Under this assumption, we derive a series of modified dispersion relations that have not been previously explored, and we analyze their implications. Our findings indicate that the scales of Lorentz violation for massive particles are proportional to their masses. Furthermore, we demonstrate that this hypothesis aligns well with existing phenomenological results regarding Lorentz violation observed in photons, neutrinos, and electrons.