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

228 Sources of SGWB−6−9−12−15−18−20 −15 −10 −5 0 5log (f / Hz)Figure 13.4. h 2 0 gw against the physical frequency f (logarithmic scales). Heref 1 = 100 kHz.Given the shape of the spectrum (see figure 13.4) one obtains in thefrequency region of interest for VIRGO the following bound:h 2 0 gw < 8 × 10 −14 , (13.29)many orders of magnitude below the sensitivity limit of the planned detectors.Finally we remark that the result reported in equation (13.27) is valid ifthe Hubble parameter during inflation is strictly constant; the calculation can bedone also for other, more realistic models, but the final result is not significantlydifferent from the one reported above. For instance, in the so-called ‘slowroll’inflation the Hubble parameter is slightly decreasing during the inflationarystage and makes the spectrum slightly tilted, instead of constant, in the radiationdominatedregion. Anyway the tilt is so small that the value of gw at interestingfrequencies is different from the one of equation (13.29) only for an order ofmagnitude (in addition this correction has the ‘wrong’ sign, i.e. it lowers thebound!).