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. We find that the tensor contribution is significant only at large angular scales (multipoles ` < ∼ 40). For standard recombination, the tensor contribution can dominate at ` < ∼ 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 (∼ 7− 9%), but the tensor fraction is negligibly small. Hence, polarization may be useful for discriminating ionization history, but is less promising as a means for detecting tensor fluctuations. Subject headings: cosmology: cosmic microwave background — cosmology: observations The cosmic microwave background (CMB) temperature anisotropy may be induced by a combination of energy density (Bardeen et al. 1983) (scalar metric) fluctuations and gravitational wave (Starobinsky 1985, Abbott and Wise 1984) (tensor metric) fluctuations. Distinguishing the scalar and tensor components is important for testing cosmological models (Davis et al. 1992, Krauss and White 1992, Salopek 1992, Sahni and Souradeep 1992, Liddle and Lyth 1992, Lucchin et al. 1992, Lidsey and Coles 1992), since only scalar metric fluctuations can grow into non-linear structures, such as galaxies, while tensor fluctuations red shift and disperse upon entering the horizon. One suggested approach for determining the tensor contribution is to compare measurements of the CMB anisotropy on scales ranging from large (< ∼ 1◦) to small (> ∼ 1◦) and take advantage of the fact that unpolarized scalar and tensor fluctuations vary differently with angular scale (Davis et al. 1992,Crittenden et al. 1993). Another suggestion has been to measure the CMB polarization since tensor fluctuations might induce a polarization significantly greater than a spectrum of purely energy density perturbations (Polnarev 1985, Ng and Ng 1993).