  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 of matter above a
certain distance 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.
