We investigate the possibility for a direct detection by future space inter
ferometers of the stochastic gravitational wave (GW) background generated d
uring the inflationary stage in a class of viable Lambda CDM BSI models. At
frequencies around 10(-3) Hz, maximal values Omega(gw)(nu) similar to 3 x
10(-15) are found, an improvement of about one order of magnitude compared
to single-field, slow-roll inflationary models. This is presumably not suff
icient in order to be probed in the near future. (C) 1999 Published by Else
vier Science B.V. All rights reserved.