  In addition to density perturbations, inflationary models of the early
universe generally predict a stochastic background of gravitational waves or
tensor fluctuations. By making use of the inflationary flow approach for single
field models and fitting the models with Monte-Carlo techniques to cosmic
microwave background (CMB) data from the {\it Wilkinson Microwave Anisotropy
Probe} (WMAP), we discuss the expected properties of the gravitational wave
background from inflation at scales corresponding to direct detection
experiments with laser interferometers in space. We complement the Monte-Carlo
numerical calculations by including predictions expected under several classes
of analytical inflationary models. We find that an improved version of {\it Big
Bang Observer} (BBO-grand) can be used to detect a gravitational wave
background at 0.1 Hz with a corresponding CMB tensor-to-scalar ratio above
10$^{-4}$. Even if the CMB tensor-to-scalar ratio were to be above 10$^{-2}$,
we suggest that BBO-grand will be useful to study inflationary models as the
standard version of BBO, with a sensitivity to a stochastic gravitational wave
background $\Omega_{\rm GW}h^2 > 10^{-17}$, will only allow a marginal
detection of the amplitude while leaving the tensor spectral index at 0.1 Hz
unconstrained. We also discuss the extent to which CMB measurements can be used
to predict the gravitational wave background amplitude in a direct detection
experiment and how any measurement of the amplitude and the spectral tilt of
the gravitational wave background at direct detection frequencies together with
the CMB tensor-to-scalar ratio can be used to establish slow-roll inflation.
