The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. We consider a scenario where Lorentz invariance is only an approximate property of equations describing a sector of matter at a given scale and superluminal sectors of matter exist related to new degrees of freedom not yet discovered experimentally. The new particles would not be tachyons: they may feel different minkowskian space-times with critical speeds much higher than c (speed of light) and behave kinematically like ordinary particles apart from the difference in critical speed. Superluminal particles may provide most of the matter at cosmic scale, and be mainly dark. We present a discussion of possible theoretical, cosmological and experimental consequences of such a scenario, with particular emphasis on problems related to the identification of dark matter.
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