  Gravitational-wave experiments with interferometers and with resonant masses
can search for stochastic backgrounds of gravitational waves of cosmological
origin. We review both experimental and theoretical aspects of the search for
these backgrounds. We give a pedagogical derivation of the various relations
that characterize the response of a detector to a stochastic background. We
discuss the sensitivities of the large interferometers under constructions
(LIGO, VIRGO, GEO600, TAMA300, AIGO) or planned (Avdanced LIGO, LISA) and of
the presently operating resonant bars, and we give the sensitivities for
various two-detectors correlations. We examine the existing limits on the
energy density in gravitational waves from nucleosynthesis, COBE and pulsars,
and their effects on theoretical predictions. We discuss general theoretical
principles for order-of-magnitude estimates of cosmological production
mechanisms, and then we turn to specific theoretical predictions from
inflation, string cosmology, phase transitions, cosmic strings and other
mechanisms. We finally compare with the stochastic backgrounds of astrophysical
origin.
