  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 (i.e. a galilean space-time). A typical example
is provided by sine-Gordon solitons in a galilean world. A "sub-world"
restricted to such solitons would be "relativistic", with the critical speed of
solitons playing the role of the speed of light. Only the study of the deep
structure of matter will unravel the actual geometry of space and time, which
we expect to be scale-dependent and determined by the properties of matter
itself. If Lorentz invariance is 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 sctructure of the space-time felt by
ordinary particles. But c, the speed of light, will not necessarily be the only
critical speed in vacuum: for instance, a superluminal sector of matter may
exist related to new degrees of freedom not yet discovered experimentally. Such
particles would not be tachyons: they may feel a different minkowskian
space-time with a critical speed larger than c and behave kinematically like
ordinary particles apart from the difference in critical speed. At speed larger
than c , they are expected to release "Cherenkov" radiation (ordinary
particles) in vacuum. We present a discussion of possible physical (theoretical
experimental) and cosmological implications of such a scenario, assuming that
the superluminal sector couples weakly to ordinary matter.
