We study the primordial gravitational wave background produced in models of single-field inflation. Using the inflationary flow approach, we investigate the amplitude of gravitational wave spectrum, ${\omega }_{\mathrm{gw}}$, in the frequency range 1 mHz–1 Hz pertinent to future space-based laser interferometers. For models that satisfy the current observational constraint on the tensor-to-scalar ratio, $r\lesssim 0.36$, we derive a strict upper bound of ${\omega }_{\mathrm{gw}}\lesssim 1.6\times {10}^{-15}$ independent of the form of the inflationary potential. Applying, in addition, the observational constraints on the spectral index $n_s$ and its running, ${\omega }_{\mathrm{gw}}$ is expected to be considerably lower than this bound unless the shape of the potential is finely tuned. We contrast our numerical results with those based on simple power-law extrapolation of the tensor power spectrum from cosmic microwave background (CMB) scales. In addition to single-field inflation, we summarize a number of other possible cosmological sources of primordial gravitational waves and assess what might be learned from direct detection experiments such as LISA, Big Bang Observer and beyond.

• Received 27 February 2006

DOI:https://doi.org/10.1103/PhysRevD.73.083511