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

String cosmology 233Figure 13.6. h 2 0 gw( f ) as a function of f per f s = 100 Hz,H s = 0.15M Pl , f 1 = 4.3 × 10 7 kHz, µ = 1.4 compared with the low- andhigh-frequency limits (from [57]).by the growth of the dilaton during the string phase; H s , the constant value of theHubble parameter during the string phase, which we expect to be of the order ofλ s −1, η s and η 1 . It is convenient to trade η s and η 1 with the associated frequenciesf s = 1/(2π R 0 |η s |), being R 0 the present value of the scale factor of the universe,and f 1 defined analogously; f 1 can be estimated to be f 1 ∼ 10 GHz and itcorresponds to the maximum amplified frequency, whereas the only constrainton f s is f s < f 1 . As shown in figure 13.6, the spectrum presents an f 3 raise forf < f s (and f s ≪ f 1 ) and a series of oscillations around the line of slope 3 − 2µfor f s < f < f 1 , while for frequency higher than f 1 the spectrum is exponentiallysuppressed, as it corresponds to the maximum of the potential in equation (13.35).In the most favourable case (µ = 1.5 and f s less than the smaller frequency in theVIRGO frequency range), the maximum value of the spectrum is reached as longas f > f s [57]h 2 0 max gw ≃ 3.0 × 10−7 (Hs0.15M Pl)(t1λ s) 2,being t 1 the time of transition to the post-big bang phase.This is just an example of possible cosmological dynamics driven by stringtheory, as it stands it cannot be identified as the prediction of string cosmology.Nevertheless the low-frequency behaviour, i.e. the power-law raise, is a quite