Quantum Gravity Phenomenology Induced in the Propagation of UHECR, a Kinematical Solution in Finsler and Generalized Finsler Spacetime

It is well-known that the universe opaque to propagation of Ultra-High-Energy Cosmic Rays (UHECRs) since these particles dissipate energy during their interacting with background fields present in universe, mainly Microwave Background (CMB) so-called GZK cut-off phenomenon. Some experimental evidence seems hint at possibility a dilation predicted opacity sphere. kinematical perturbations caused by supposed quantum gravity (QG) effects can modify foreseen horizon. The introduction Lorentz Invariance Violation indeed reduce, and some cases making negligible, CMB-UHECRs interaction probability. In this work, we explore induced modified kinematics UHECR lightest component phenomenology from QG perspective. We geometrical description massive fermions structure spacetime order introduce covariance modification. are amended, modifying dispersion relations free context covariance-preserving framework. This requires more general geometry than usual Riemannian one, indicating, for instance, Finsler construction related generalized as ideal candidates. Finally investigate correlation between magnitude modification attenuation length photopion production process cut-off, demonstrating horizon be dilated even theory does not require any privileged reference frame.