Polarization of the Microwave Background due to Primordial Gravitational Waves

The contribution of gravitational wave (tensor metric) and energy density (scalar metric) fluctuations to the cosmic microwave background polarization is computed by numerically solving the relativistic radiation transfer equations. We find that the tensor contribution is significant only at large angular scales (multipoles $\ell \lta 40$). For standard recombination, the tensor contribution can dominate at $\ell \lta 40$; however, the effect would be difficult to detect since the total (scalar plus tensor) polarization is $< 1$\%. For models with late reionization, the total large angular scale polarization is large ($\sim 7-9$\%), but the tensor fraction is negligibly small. Hence, polarization may be useful for discriminating ionization history, but is much less promising as a means for detecting tensor fluctuations.