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

The relic graviton background 313Figure 16.11. Peak and end point of the spectrum in minimal and non-minimal models.In the minimal models the position of the peak is fixed. Actually, whatis really fixed, in string cosmology, is the maximal height of the peak, but notnecessarily the position in frequency, and it is not impossible, in more complicatednon-minimal models, to shift the peak at lower frequencies.In minimal models, in fact, the beginning of the radiation phase coincideswith the end of the string phase. We may also consider models, however, in whichthe dilaton coupling gs2 = exp(φ) is still small at the end of the high curvaturephase, and the radiation era begins much later, when g s 2 ∼ 1, after an intermediatedilaton-dominated regime. The main difference between the two cases is that inthe second case the effective potential which amplifies tensor perturbations is nonmonotonic[59], so that there are high-frequency modes re-entering the horizonbefore the radiation era. As a consequence, the perturbation spectrum is also nonmonotonic,and the peak does not coincide any longer, in general, with the endpoint of the spectrum (see also [71]), as illustrated in figure 16.11.For minimal models the peak is around 100 GHz, for non-minimal modelsit could be at lower frequencies. These are good news from an experimentalpoint of view, of course, but non-minimal models seem to be less natural, atleast from a theoretical point of view. The boxes around the peak, appearingin figure 16.11, represent the uncertainty in the position of the peak due to ourpresent ignorance about the precise value of the ratio M s /M p (for the illustrativepurpose of figure 16.11, the ratio is assumed to vary in the range 0.1–0.01). Thewavy line, in the high frequency branch of the spectrum, represents the fact thatthe spectrum associated with the string phase could be monotonic on average,but locally oscillating [72]. Finally, the lower strip, labelled by δs = 99%,represents the fact that even the height of the peak could be lower than expected,if the produced gravitons have been diluted by some additional reheating phase,occurring well below the string scale, during the standard evolution.