A particularly simple Lorentz-violating modification of the Maxwell theory of photons maintains gauge invariance, $CPT$, and renormalization. This modified Maxwell theory, coupled to standard Dirac particles, involves 19 dimensionless “deformation parameters.” Ten of these parameters lead to birefringence and are already tightly constrained by astrophysics. New bounds on the remaining nine nonbirefringent parameters can be obtained from the absence of vacuum Cherenkov radiation for ultrahigh-energy cosmic rays (UHECRs). Using selected UHECR events recorded at the Pierre Auger Observatory and assigning pseudorandom directions (i.e., assuming large-scale isotropy), Cherenkov bounds are found at the ${10}^{-18}$ level, which improve considerably upon current laboratory bounds. Future UHECR observations may reduce these Cherenkov bounds to the ${10}^{-23}$ level.

• Received 16 September 2007

DOI:https://doi.org/10.1103/PhysRevD.77.016002