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Inflation predicts a stochastic background of gravitational waves over abroad range of frequencies, from those accessible with cosmic microwavebackground (CMB) measurements, to those accessible directly withgravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currentlyunder study. In a previous paper [Phys. Rev. D73, 023504 (2006)] we connectedCMB constraints to the amplitude and tensor spectral index of the inflationarygravitational-wave background (IGWB) at BBO frequencies for four classes ofmodels of inflation by directly solving the inflationary equations of motion.Here we extend that analysis by including results obtained in the WMAPthird-year data release as well as by considering two additional classes ofinflationary models. As often noted in the literature, the recent indicationthat the primordial density power-spectrum has a red spectral index implies(with some caveats) that the amplitude of the IGWB may be large enough to beobservable in the CMB polarization. Here we also explore the implications forthe direct detection of the IGWB.

The inflationary gravitational-wave background and measurements of the scalar spectral index