Inflationary gravitational-wave background and measurements of the scalar spectral index

Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA's Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D 73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral tilt of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. Here we extend that analysis by including results obtained in the Wilkinson Microwave Anisotropy Probe third-year data release as well as by considering two additional classes of inflationary models. As often noted in the literature, the recent indication that 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 be observable in the CMB polarization. Here we also explore the implications for the direct detection of the IGWB.