ABSTRACT
This is a contracted version of a series of lectures for graduate and undergraduate students given at the ‘VI Seminario Nazionale di Fisica Teorica’ (Parma, September 1997), at the Second International Conference ‘Around VIRGO’ (Pisa, September 1998), and at the Second SIGRAV School on ‘Gravitational Waves in Astrophysics, Cosmology and String Theory’ (Center ‘A. Volta’, Como, April 1999). The aim is to provide an elementary, self-contained introduction to string cosmology and, in particular, to the background of relic cosmic gravitons predicted in the context of the so-called ‘pre-big bang’ scenario. No special preparation is required besides a basic knowledge of general relativity and of standard (inflationary) cosmology. All the essential computations are reported in full details either in the main text or in the appendices. For a deeper and more complete approach to the pre-big bang scenario the interested reader is referred to the updated collection of papers available at https://www.to.infn.it/∼gasperin/.
