Massive string modes and non-singular pre-big-bang cosmology

Perturbative alpha' corrections to the low energy string effective action have been recently found to have a potentially regularizing effect on the singularity of the lowest order pre-big-bang solutions. Whether they actually regularize it, however, cannot be determined working at any finite order in a perturbative expansion in powers of the string constant alpha', because of scheme dependence ambiguities. Physically, these corrections are dominated by the integration over the first few massive string states. Very massive string modes, instead, can have a regularizing effect which is non-perturbative in alpha' and which basically comes from the fact that in a gravitational field with Hubble constant H they are produced with an effective Hawking temperature T = Hl(2 pi), and an infinite production rate would occur if this temperature exceeded the Hagedorn temperature. We discuss technical and conceptual difficulties of this non-perturbative regularization mechanism. (C) 1998 Elsevier Science B.V.