Why should we be concerned with the polarization of the cosmic microwave background (CMB) anisotropies? That the CMB anisotropies are polarized is a fundamental prediction of the gravitational instability paradigm. Under this paradigm, small fluctuations in the early universe grow into the large scale structure we see today. If the temperature anisotropies we observe are indeed the result of primordial fluctuations, their presence at last scattering would polarize the CMB anisotropies themselves. The verification of the (partial) polarization of the CMB on small scales would thus represent a fundamental check on our basic assumptions about the behavior of fluctuations in the universe, in much the same way that the redshift dependence of the CMB temperature is a test of our assumptions about the background cosmology.
Furthermore, observations of polarization provide an important tool for reconstructing the model of the fluctuations from the observed power spectrum (as distinct from fitting an a priori model prediction to the observations). The polarization probes the epoch of last scattering directly as opposed to the temperature fluctuations which may evolve between last scattering and the present. This localization in time is a very powerful constraint for reconstructing the sources of anisotropy. Moreover, different sources of temperature anisotropies (scalar, vector and tensor) give different patterns in the polarization: both in its intrinsic structure and in its correlation with the temperature fluctuations themselves. Thus by including polarization information, one can distinguish the ingredients which go to make up the temperature power spectrum and so the cosmological model.
Finally, the polarization power spectrum provides information complementary to the temperature power spectrum even for ordinary (scalar or density) perturbations. This can be of use in breaking parameter degeneracies and thus constraining cosmological parameters more accurately. The prime example of this is the degeneracy, within the limitations of cosmic variance, between a change in the normalization and an epoch of ``late'' reionization.
Yet how polarized are the fluctuations? The degree of linear polarization is directly related to the quadrupole anisotropy in the photons when they last scatter. While the exact properties of the polarization depend on the mechanism for producing the anisotropy, several general properties arise. The polarization peaks at angular scales smaller than the horizon at last scattering due to causality. Furthermore, the polarized fraction of the temperature anisotropy is small since only those photons that last scattered in an optically thin region could have possessed a quadrupole anisotropy. The fraction depends on the duration of last scattering. For the standard thermal history, it is on a characteristic scale of tens of arcminutes. Since temperature anisotropies are at the level, the polarized signal is at (or below) the level, or several K, representing a significant experimental challenge.
Our goal here is to provide physical intuition for these issues. For mathematical details, we refer the reader to [Kamionkowski et al.] (1997), [Zaldarriaga & Seljak] (1997), [Hu & White] (1997) as well as pioneering work by [Bond & Efstathiou] (1984) and [Polnarev] (1985). The outline of the paper is as follows. We begin in §2 by examining the general properties of polarization formation from Thomson scattering of scalar, vector and tensor anisotropy sources. We discuss the properties of the resultant polarization patterns on the sky and their correlation with temperature patterns in §3. These considerations are applied to the reconstruction problem in §4. The current state of observations and techniques for data analysis are reviewed in §5. We conclude in §6 with comments on future prospects for the measurement of CMB polarization.