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

210 Generalities on the stochastic GW backgroundIf the integral cannot exceed these values, also its positive definite integrandh 2 0 gw( f ) cannot exceed it over an appreciable interval of frequencies, ln f ∼1. One might still have, in principle, a very narrow peak in h 2 0 gw( f ) at somefrequency f , with a peak value larger than say 10 −5 , while still its contributionto the integral could be small enough. However, apart from the fact thatsuch behaviour seems rather implausible, or at least is not suggested by anycosmological mechanism, it would also be probably of little help in the detectionat broadband detectors like VIRGO, because even if we gain in the height of thesignal we lose because of the reduction of the useful frequency band f , seeequation (12.12).These numbers, therefore, give a first idea of what can be considered aninteresting detection level for h 2 0 gw( f ), which should be at least a few times10 −6 , especially considering that the bound (12.64) refers not only to gravitationalwaves, but to all possible sources of energy which have not been included, likeparticles beyond the standard model, primordial black holes, etc.As a final remark, we note that a very weak bound in the region f ∼1 kHz has been obtained from the analysis of correlation between bar detectors.Preliminary results on a NAUTILUS–EXPLORER correlation, using 12 hours ofdata, have been reported in [27], and give h 2 0 gw( f = 920 Hz) ∼ 120.