Relic gravitons from the pre-big bang: what we know and what we do not know

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I discuss the status of present knowledge about a possible background of relic gravitons left by an early, pre-big bang cosmological epoch, whose existence in the past of our Universe is suggested by the duality symmetries of string theory.
34 pages, LATEX, 12 figures included using epsf. See also http://www.to.infn.it/teorici/gasperini/

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