The energy spectrum of the cosmic radiation (not CMB) is limited to both sides.
I know about the GZK-cutoff at high energies. Basically the interaction probability for photons of energies above 10^20 eV becomes so high, that all have interacted before they can reach us.
But why is there a limit at lower energies? Earth magnetic field and/or athmosphere, radiation belt? Perhaps someone can explain that to me.