  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.
