Cosmological Implications of a Possible Class of Particles Able to Travel Faster than Light

We discuss the possible cosmological implications of a class of superluminal particles, in a scenario where: a) Lorentz invariance is only an approximate property of the equations of a sector of matter; b) several critical speeds of matter in vacuum exist. The Big Bang scenario and the evolution of the very early universe, as well as large scale structure, can be strongly influenced by the new particles.