Testing Lorentz invariance with the ultrahigh energy cosmic ray spectrum

The Greisen-Zatsepin-Kuzmin cutoff predicted at the ultrahigh energy cosmic ray spectrum has been observed by the HiRes and Auger experiments. The results put severe constraints on the effect of Lorentz invariance violation (LIV), which has been introduced to explain the absence of the Greisen-Zatsepin-Kuzmin cutoff indicated in the AGASA data. Assuming a homogeneous source distribution with a single power-law spectrum, we calculate the ultrahigh energy cosmic ray spectrum observed on the Earth by taking photopion production, e⁺e^- pair production, and the adiabatic energy loss into account. The effect of LIV is also taken into account in the calculation. By fitting the HiRes monocular spectra and the Auger combined spectra, we show that the LIV parameter is constrained to ξ=-0.8_-0.5^+3.2×10^-23 and 0.0_-0.4^+1.0×10^-23, respectively, which is very consistent with strict Lorentz invariance up to the highest energy.