Constraints on the Pre-Big Bang scenario from a cosmological interpretation of the NANOGrav data

We discuss a recently proposed fit of the 15-year data set obtained from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) in terms of a relic stochastic background of primordial gravitons, produced in the context of the string cosmology pre-big bang scenario. We show that such interpretation cannot be reconciled with a phenomenologically viable minimal version of such scenario, while it can be allowed if one considers an equally viable but generalised, non-minimal version of pre-big bang evolution. Maintaining the $S$-duality symmetry throughout the high-curvature string phase is possible although somewhat disfavoured. The implications of this non-minimal scenario for the power spectrum of curvature perturbations are also briefly discussed.