Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment

TL;DR

This paper investigates how the GRAAL experiment constrains spacetime anisotropy and Lorentz violation using Finsler geometry, finding that anisotropy is limited to less than 10^{-14} and linking Finslerian models to the SME framework.

Contribution

It introduces a Finsler geometric approach to model spacetime anisotropy and Lorentz violation, connecting it with the minimal standard model extension.

Findings

Spacetime anisotropy constrained to less than 10^{-14} by GRAAL.

Finslerian photon sector can represent the minimal SME photon sector.

Finsler geometry provides a viable framework for LIV analysis.

Abstract

The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy. In this paper, the Lorentz invariance violation (LIV) of the photon sector is investigated in the locally Minkowski spacetime. The locally Minkowski spacetime is a class of flat Finsler spacetime and refers a metric with the anisotropic departure from the Minkowski one. The LIV matrices used to fit the experimental data are represented in terms of these metric deviations. The GRAAL experiment constrains the spacetime anisotropy to be less than \(10^{-14}\). In addition, we find that the simplest Finslerian photon sector could be viewed as a geometric representation of the photon sector in the minimal standard model extension (SME).