String cosmology and relic gravitational radiaton

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String theory counterparts to Einstein's gravity, cosmology and inflation are described. A very tight upper bound on the Cosmic Gravitational Radiation Background (CGRB) of standard inflation is shown to be evaded in string cosmology, while an interesting signal in the phenomenologically interesting frequency range is all but excluded. The generic features of such a stringy CGRB are presented.
16 pages, LATEX, five figure included using epsf, appended as ps file. A complete collection of papers and references on the pre-big-bang scenario in string cosmology is available at http://www.to.infn.it/teorici/gasperini/

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