  We discuss the possible relevance of gravitational-wave (GW) experiments for
physics at very high energy. We examine whether, from the experience gained
with the computations of various specific relic GW backgrounds, we can extract
statements and order of magnitude estimates that are as much as possible
model-independent, and we try to distinguish between general conclusions and
results related to specific cosmological mechanisms. We examine the statement
that the Virgo/LIGO experiments probe the Universe at temperatures $T\sim
10^{7}-10^{10}$ GeV (or timescales $t\sim 10^{-20}-10^{-26}$ sec) and we
consider the possibility that they could actually probe the Universe at much
higher energy scales, including the typical scales of grand unification, string
theory and quantum gravity. We consider possible scenarios, depending on how
the inflationary paradigm is implemented. We discuss the prospects for
detection with present and planned experiments. In particular, a second Virgo
interferometer correlated with the planned one, and located within a few tens
of kilometers from the first, could reach an interesting sensitivity for
stochastic GWs of cosmological origin.
