Imaging parity-violation in the CMB

Abstract

Correlations of polarization components in the coordinate frame are a natural basis for searches of parity-violating modes in the Cosmic Microwave Background (CMB). This fact can be exploited to build estimators of parity-violating modes that are {\sl local} and robust with respect to partial-sky coverage or inhomogeneous weighting. As an example application of a method based on these ideas we develop a peak stacking tool that isolates the signature of parity-violating modes. We apply the tool to {\sl Planck} maps and obtain a constraint on the monopole of the polarization rotation angle $\alpha < 0.72$ degrees at $95\%$ We also demonstrate how the tool can be used as a local method for reconstructing maps of direction dependent rotation $\alpha(\hat {n})$.