Using Ultrahigh-Energy Cosmic Rays and Air Showers to Test Lorentz Invariance Within Modified Maxwell Theory

Cosmic rays and air showers at ultrahigh energy are unique tools to test the validity of Lorentz invariance. A brief overview is given on such tests focusing on isotropic, non-birefringent Lorentz violation in the photon sector. Based on the apparent absence of vacuum Cherenkov radiation and photon decay, the Lorentz-violating parameter κ is bounded to −0.6 · 10⁻²⁰ < κ < 6 · 10⁻²⁰ (98% CL). We report an updated limit from cosmic-ray photon observations and preliminary results on testing vacuum Cherenkov radiation in air showers.