As high energy protons travel through expanding space do we measure some physical difference depending on how far they travel before reaching us?
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$\begingroup$ Related physics.stackexchange.com/q/133246 $\endgroup$– ProfRobCommented Aug 27, 2015 at 7:56
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Cosmic rays have a de Broglie wavelength. The de Broglie wavelength is redshifted by the expansion of space in the same way that the wavelength of light is redshifted. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse of the scale factor.
This means that the energies of any cosmic rays we detect from extragalactic sources at large redshifts would have been produced with correspondingly higher energies.
