Detectability of microwave background polarization

Measurement of the amplitudes of both the E and B components of the CMB polarization will open new windows into the early Universe. Using a Fisher-matrix formalism, we calculate the required sensitivities and observing times for an experiment to measure the amplitudes of both E and B components as a function of sky coverage, taking full account of the fact that the two components cannot be perfectly separated in an incomplete sky map. We also present a simple approximation scheme that accounts for mixing of E and B components in computing predicted errors in the E-component power spectrum amplitude. In an experiment with small sky coverage, mixing of the two components increases the difficulty of detecting the subdominant B component by a factor of two or more in observing time; however, for larger survey sizes the effect of mixing is less pronounced. As a result, the optimal experimental setup for detecting the B component must cover an area of sky significantly larger than is found when mixing is neglected. Surprisingly, mixing of E and B components can enhance the detectability of the E component by increasing the effective number of independent modes that probe this component. The formalism presented in this paper can be used to explore ways in which survey geometry and nonuniform noise due to uneven sky coverage will affect detectability of the two components.