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.Comment: 5 pages, to be published in the Proceedings of the Fourth
International Workshop on Theoretical and Phenomenological Aspects of
Underground Physics, Toledo (Spain) September 17-21 199