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 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 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 ${\Omega }_{\mathrm{GW}}{h}^2>{10}^{-17}$, will only allow a marginal detection of the amplitude while leaving the tensor spectral index at 0.1 Hz unconstrained. Also, inflationary models with a large tensor-to-scalar ratio predict a substantial negative tensor spectral index such that the gravitational wave amplitude is damped at direct detection frequencies. 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.

• Received 6 October 2006

DOI:https://doi.org/10.1103/PhysRevD.74.123509