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

314 Elementary introduction to pre-big bang cosmologylog 10( Gh 2 100)log10(/ Hz)Figure 16.12. Allowed region for the spectrum of vacuum fluctuations in string cosmologyand in standard inflation, compared with other relic spectra of primordial origin.This last effect can be parametrized in terms of δs, which is the fraction ofpresent entropy density in radiation, due to such additional, low-scale reheating.The position of the peak then depends on δs as [33]:( ) 1/2 Msω 1 (t 0 ) ≃ T 0 (1 − δs) 1/3 ,M p( ) 2 G (ω 1 , t 0 ) ≃ 7 × 10 −5 h −2 Ms100(1 − δs) 4/3 , (16.107)M pwhere T 0 = 2.7K≃ 3.6 × 10 11 Hz. Such a dependence is not dramatic, however,because even for δs = 99% the peak keeps well above the standard inflationaryprediction, represented by the line labelled ‘de Sitter’ in figure 16.11.Given the various theoretical uncertainties, the best we can do, at present, isto define the maximal allowed region for the expected graviton background, i.e.the region spanned by the spectrum when all its parameters are varied. Such aregion is illustrated in figure 16.12, for the phenomenologically interesting highfrequencyrange. The figure emphasizes the possible, large enhancement (of abouteight orders of magnitude) of the intensity of the background in string cosmology,with respect to the standard inflationary scenario.It may be useful to stress again the reason of such enhancement. Inthe standard inflationary scenario the graviton spectrum is decreasing, thenormalization is imposed at low frequency, and the peak value is controlled by