Response of VIRGO detectors to pre-big-bang gravitons

The sensitivity achievable by a pair of VIRGO detectors to stochastic and i sotropic gravitational wave backgrounds produced in pre-big-bang models is discussed in view of the development of a second VIRGO interferometer. We d escribe a semi-analytical technique allowing to compute the signal-to-noise ratio for (monotonic or non-monotonic) logarithmic energy spectra of relic gravitons of arbitrary slope. We apply our results to the case of two corr elated and coaligned VIRGO detectors and we compute their achievable sensit ivities. We perform our calculations both for the usual case of minimal str ing cosmological scenario and in the case of a non-minimal scenario (origin ally suggested by Gasperini) where a long dilaton dominated phase is presen t prior to the onset of the ordinary radiation dominated phase. In this fra mework, we investigate possible improvements of the achievable sensitivitie s by selective reduction of the thermal contributions (pendulum and pendulu m's internal modes) to the noise power spectra of the detectors. Since a re duction of the shot noise does not increase significantly the expected sens itivity of a VIRGO pair (in spite of the relative spatial location of the t wo detectors) our findings support the experimental efforts directed toward s a substantial reduction of thermal noise.