Have we already detected astrophysical symptoms of space-time noncommutativity?

We discuss astrophysical implications of κ-Minkowski space-time, in which space-time noncommutativity appears. We first derive a velocity formula for particles based on the motion of a wave packet. The result is that a massless particle moves at a constant speed as in the usual Minkowski space-time, which implies that an arrival time analysis of γ rays from Markarian (Mk) 421 does not exclude space-time noncommutativity. Based on this observation, we analyze reaction processes in κ-Minkowski space-time which are related to the puzzling detection of extremely high-energy cosmic rays above the Greisen-Zatsepin-Kuzmin cutoff and of high-energy (∼20 TeV) γ rays from Mk 501. In these analyses, we take into account the ambiguity of the momentum conservation law which cannot be determined uniquely from a mathematical viewpoint. We find that peculiar types of momentum conservation law with some length scale of noncommutativity above a critical length scale can explain such puzzling detection. We also obtain stringent constraints on the length scale of noncommutativity and the freedom of the momentum conservation law.