Observing air showers from cosmic superluminal particles

The Poincare relativity principle has been tested at low energy with great accuracy, but its extrapolation to very high-energy phenomena is much less well established. Lorentz symmetry can be broken at Planck scale due to the renormalization of gravity or to some deeper structure of matter: we expect such a breaking to be a very high energy and very short distance phenomenon. If textbook special relativity is only an approximate property of the equations describing a sector of matter above some critical distance scale, an absolute local frame (the 'vacuum rest frame', VRF) can possibly be found and superluminal sectors of matter may exist related to new degrees of freedom not yet discovered experimentally. The new superluminal particles ('superbradyons', i.e. bradyons with superluminal critical speed) would have positive mass and energy, and behave kinematically like 'ordinary' particles (those with critical speed in vacuum equal to c, the speed of light) apart from the difference in critical speed (we expect ci>>c, where ci is the critical speed of a superluminal sector). They may be the ultimate building blocks of matter. At speed v>c, they are expected to release ''Cherenkov'' radiation ('ordinary' particles) in vacuum. Superluminal particles could provide most of the cosmic (dark) matter and produce very high-energy cosmic rays. We discuss: a) the possible relevance of superluminal matter to the composition, sources and spectra of high-energy cosmic rays; b) signatures and experiments allowing to possibly explore such effects. Very large volume and unprecedented background rejection ability are crucial requirements for any detector devoted to the search for cosmic superbradyons. Future cosmic-ray experiments using air-shower detectors (especially from space) naturally fulfil both requirements