On Numerical Simulations of Intergalactic Electromagnetic Cascades with Lorentz Invariance Violation

Lorentz invariance violation (LIV) is a proposed phenomenon where Lorentz symmetry is violated at high energies, potentially affecting particle dynamics and interactions. We use numerical simulations with the CRPropa framework to investigate LIV in gamma-ray-induced electromagnetic cascades, specifically studying how it impacts cascading electrons and photons undergoing pair production and inverse Compton scattering. Our detailed analysis of the simulation results, compared with existing theoretical models, reveals that LIV can significantly alter the behavior of both components of the cascade, photons and electrons, resulting in specific signatures in measured fluxes that could be observed in high-energy gamma-ray observations. These insights are crucial for ongoing searches for LIV and for the development of theoretical models incorporating LIV effects.