(ed.). Gravitational waves (IOP, 2001)(422s).

The relic graviton background 311Figure 16.8. Graviton spectra in the standard inflationary scenario.Figure 16.9. A minimal model of the pre-big bang background.(for power-inflation the bound is even stronger [31]).This bound applies to all models characterized by a flat or decreasingspectrum. The bound can be evaded, however, if the spectrum is growing, like inthe string cosmology context. To illustrate this point, let us consider the simplestclass of the so-called ‘minimal’ pre-big bang models, characterized by threemain kinematic phases [32, 44]: an initial low-energy, dilaton-driven phase, anintermediate high-energy ‘string’ phase, in which α ′ and loop corrections becomeimportant, and a final standard, radiation-dominated phase (see figure 16.9). Thetimescale η s marks the transition to the high-curvature phase, and the timescaleη 1 , characterized by a final curvature of order one in string units, marks thetransition to the radiation-dominated cosmology.