The overall cosmic-ray spectrum showing the average slope of the spectrum over three important intervals: below the “knee” at 1015 eV, from the “knee” to the “ankle” just below 1019 eV, and around the predicted GZK cutoff near 1019–1020 eV. (Lower inset) The high-energy data measured at the Auger telescope (the white triangles indicate upper limits only) . Blue lines are guides to the eye, drawn using the spectral indices from Ref.  (Auger) above the ankle, and the spectral index from Ref.  (HiRes) below the ankle. The upper inset sketches the interaction between a cosmic-ray particle (proton or neutron) and a photon, γ, in the cosmic microwave background that results in the photoproduction of secondary π mesons via a Δ resonance.