Signature of Gravity Waves in the Polarization of the Microwave Background

Using spin-weighted decomposition of polarization in the cosmic microwave background (CMB) we show that a particular combination of Stokes $Q$ and $U$ parameters vanishes for primordial fluctuations generated by scalar modes, but does not for those generated by primordial gravity waves. Because of this gravity wave detection is not limited by cosmic variance as in the case of temperature fluctuations. We present the exact expressions for various polarization power spectra, which are valid on any scale. Numerical evaluation in inflation-based models shows that the expected signal is of the order of 0.5 $\mu$K, which could be directly tested in future CMB experiments.