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

234 Sources of SGWBgeneral feature which belongs to any PBB-dictated spectrum of gravitationalwaves.13.3.2 Observational bounds to the spectrumBecause of the power raise of the spectrum for low frequency the COBE boundis easily evaded (see figure 13.7) and the same statement holds for the constraintderived from pulsar timing observation as long as f s < 10 −7 Hz. The moststringent bound is then the nucleosynthesis one given in section 12.5. In the mostfavourable case (a flat spectrum gw ( f ) = maxgw for f s < f < f 1 , which meansµ = 1.5) that bound translates intoh 2 0 max gw ln f 1< 6.3 × 10 −6 .f sIn order to have experimentally interesting values, the spectrum must have alreadyreached the maximum value gwmax in the VIRGO frequency range. Under thisassumption, a favourable choice of f s is 100 Hz, that leads toh 2 0 max gw < 3.2 × 10−7 . (13.36)The effect of the observational bound on the parameters of the model is displayedin figure 13.8, where the independent parameters are chosen to be η s /η 1 = f 1 /f sand β (see equation (13.33)).Figure 13.7. h 2 0 gw( f ) as a function of f per f s = 10 Hz, f 1 = 4.3 × 10 7 kHz, µ = 1.5compared with observational bounds (from [57]).