Constraining a spatially dependent rotation of the cosmic microwave background polarization

Following Kamionkowski ( 2008), a quadratic estimator of the rotation of the plane of polarization of the cosmic microwave background (CMB) is constructed. This statistic can estimate a spatially varying rotation angle alpha(n). We use this estimator to quantify the prospects of detecting such a rotation field with forthcoming experiments. For PLANCK and CMBPol experiments, we find that the estimator containing the product of the E and B components of the polarization field is the most sensitive. The variance of this EB estimator N(L) is roughly independent of the multipole L and is only weakly dependent on the instrumental beam. For FWHM of the beam size Theta(fwhm) similar to 5'-50' and instrument noise Delta(p) similar to 5-50 mu K-arcmin, the scaling of variance N(L) can be fitted by a power law N(L) = 3.3 X 10(-7) Delta(2)(p) Theta(1.3)(fwhm) deg(2). For small instrumental noise Delta(p) <= 5 mu K-arcmin, the lensing B modes become important, saturating the variance to similar to 10(-6) deg(2) even for an ideal experiment. Upcoming experiments like PLANCK will be able to detect a power spectrum of the rotation angle, C-alpha alpha(L), as small as 0.01 deg(2), while futuristic experiments like CMBPol will be able to detect rotation angle power spectrum as small as 2.5 X 10(-5) deg(2). We discuss the implications of such constraints, both for the various physical effects that can rotate the polarization as photons travel from the last scattering surface as well as for constraints on instrumental systematics that can also lead to a spurious rotation signal. Rotation of the CMB polarization generates B modes which will act as contamination for the primordial B-mode detection. We discuss an application of our estimator to derotate the CMB to increase the sensitivity for the primordial B modes.