Detectability of Inflationary Gravitational Waves with Microwave Background Polarization

Inflation predicts specific relations between the amplitudes and spectral indices of the primordial spectrum of density (scalar metric) perturbations and gravitational waves (tensor metric perturbations). Detection of a stochastic gravitational-wave background is essential for identifying this unmistakable signature. Polarization of the cosmic microwave background can isolate these tensor modes in a model-independent way and thereby circumvent the cosmic-variance limit to detecting a small tensor signal with only a temperature map. Here we assess the detectability of a gravity-wave background with a temperature and polarization map. For detector sensitivities better than $10-20 \mu K \sqrt{sec}$, the sensitivity to a tensor signal is always dominated by the polarization map. With a detector sensitivity of order $1 \mu K \sqrt{sec}$, polarization could improve on a temperature-map sensitivity to tensor modes by two to three orders of magnitude. Even a small amount of reionization substantially enhances tensor-mode detectability. We also argue that the sensitivity of the Planck Surveyor to tensor modes is significantly improved with polarization, even taking into account the resulting degradation of the intensity determination in the high-frequency channels.