Superluminal particles are not excluded by particle physics. The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. Matter made of solutions of Lorentz-invariant equations would feel a relativistic space-time even if the actual space-time had a quite different geometry (f.i. a galilean space-time). If Lorentz invariance is only a property of equations describing a sector of matter at a given scale, an absolute frame (the "vacuum rest frame") may exist without contradicting the minkowskian structure felt by ordinary particles. Then c , the speed of light, will not necessarily be the only critical speed in vacuum and superluminal sectors of matter may equally exist feeling space-times with critical speeds larger than c . We present a discussion of possible cosmological implications of such a scenario, assuming that the superluminal sectors couple weakly to ordinary matter. The universality of the equivalence between inertial and gravitational mass will be lost. The Big Bang scenario will undergo important modifications, and the evolution of the Universe may be strongly influenced by superluminal particles.