  In the light of the recent results concerning CMB observations and GW
detection we address the question of whether it is possible, in a
self-consistent inflationary framework, to simultaneously generate a spectrum
of scalar metric perturbations in agreement with Planck data and a stochastic
background of primordial gravitational radiation compatible with the design
sensitivity of aLIGO/Virgo and/or eLISA. We suggest that this is possible in a
string cosmology context, for a wide region of the parameter space of the
so-called pre-big bang models. We also discuss the associated values of the
tensor-to-scalar ratio relevant to the CMB polarization experiments. We
conclude that future, cross-correlated results from CMB observations and GW
detectors will be able to confirm or disprove pre-big bang models and -- in any
case -- will impose new significant constraints on the basic string
theory/cosmology parameters.
