Polarization pursuers' guide

We calculate the detectability of the polarization of the cosmic microwave background (CMB) as a function of the sky coverage, angular resolution, and instrumental sensitivity for a hypothetical experiment. We consider the gradient component of the polarization from density perturbations (scalar modes) and the curl component from gravitational waves (tensor modes). We show that the amplitude (and thus the detectability) of the polarization from density perturbations is roughly the same in any model as long as the model fits the big-bang-nucleosynthesis (BBN) baryon density and degree-scale anisotropy measurements. The degree-scale polarization is smaller (and accordingly more difficult to detect) if the baryon density is higher. We show that the sensitivity to the polarization from density perturbations and gravitational waves is improved (by a factor of 30) in a fixed-rime experiment with a deeper survey of a smaller region of sky.