Loop Quantum Gravity and Ultra High Energy Cosmic Rays

There are two main sets of data for the observed spectrum of ultra high energy cosmic rays (those cosmic rays with energies greater than $\sim 4 \times 10^{18}$ eV), the High Resolution Fly's Eye (HiRes) collaboration group observations, which seem to be consistent with the predicted theoretical spectrum (and therefore with the theoretical limit known as the Greisen-Zatsepin-Kuzmin cutoff), and the observations from the Akeno Giant Air Shower Array (AGASA) collaboration group, which reveal an abundant flux of incoming particles with energies above $1 \times 10^{20}$ eV violating the Greisen-Zatsepin-Kuzmin cutoff. As an explanation of this anomaly it has been suggested that quantum-gravitational effects may be playing a decisive role in the propagation of ultra high energy cosmic rays. In this article we take the loop quantum gravity approach. We shall provide some techniques to establish and analyze new constraints on the loop quantum gravity parameters arising from both sets of data, HiRes and AGASA . We shall also study their effects on the predicted spectrum for ultra high energy cosmic rays. As a result we will state the possibility of reconciling the AGASA observations.