Cosmic rays are particles whose existence is revealed by the observation of electromagnetic cascades, i.e. showers of secondary charged particles, originating in the upper atmosphere and reaching the Earth's surface. Their energy spectrum, (more information can be obtained by the HiRes experiment website, by clicking on the figure at the top-left of your screen) covers about 11 orders of magnitude and extends up to extreme energies, above 10²⁰ eV.

The origin of the ultra high energy cosmic rays (UHECRs),I.e. cosmic rays with energies above 4 x 10¹⁹eV, is a mystery. In fact, there are very few astrophysical sources that can accelerate particles at these energies, and the arrival directions, apparently isotropic, do not have any obvious astronomical counterpart.

Click on the figure for additional information on cosmic rays (external link).

Image from http://ast.leeds.ac.uk/haverah/dets.shtml

Wherever UHECRs are produced, they are expected to interact with the background radiation of the Universe. If UHECRs are protons, they interact with the photons of the cosmic microwave background by photopion production; this would  predict a break in the cosmic ray flux, the so-called GZK cut-off, unless the sources of UHECR above the GZK are nearer than about 50 Mpc.

The GZK cut-off has not been observed by the experiments such as Fly's Eye,  Haverah Park, Yakutsk, and AGASA. However, currently there seems to be a disagreement specifically between  the AGASA ground array which detected about 10 events above 10²⁰ eV, as opposed to about 2 expected from the GZK cut-off, and the HiRes fluorescence detector which seems consistent with a cut-off.

The resolution of this problem may have to await the completion of the Pierre Auger project which will combine the two existing complementary detection techniques, I.e. ground arrays and fluorescence detectors.

Excellent introductions to this subject can  be found here.

Our publications on cosmic rays can be found here.

References:

G.Bertone, C.Isola, M.Lemoine, G.Sigl, Phys.Rev.D66:103003,2002

C.Isola, G.Sigl, G.Bertone, astro-ph/0312374