High precision modeling of polarized signals: Moment expansion method generalized to spin-2 fields

TL;DR

This paper introduces a generalized spin-moment expansion method for modeling polarized signals in the CMB, improving the accuracy of foreground removal by accounting for polarization angle variations.

Contribution

The paper extends the intensity moment expansion to spin-2 fields, providing a new framework for polarization modeling in CMB analysis.

Findings

Spin-moment expansion relates moments to spectral parameters and polarization angles.

The method captures frequency dependence of polarization angles.

Illustrative examples demonstrate the method's applicability.

Abstract

The modeling and removal of foregrounds poses a major challenge to searches for signals from inflation using the cosmic microwave background (CMB). In particular, the modeling of CMB foregrounds including various spatial averaging effects introduces multiple complications that will have to be accounted for in upcoming analyses. In this work, we introduce the generalization of the intensity moment expansion to the spin-2 field of linear polarization: the spin-moment expansion. Within this framework, moments become spin-2 objects that are directly related to the underlying spectral parameters and polarization angle distribution functions. In obtaining the required expressions for the polarization modeling, we highlight the similarities and differences with the intensity moment methods. A spinor rotation in the complex plane with frequency naturally arises from the first order moment when the signal contains both spectral parameters and polarization angle variations. Additional dependencies are introduced at higher order, and we demonstrate how these can be accounted with several illustrative examples. Our new modeling of the polarized signals reveals to be a powerful tool to model the frequency dependence of the polarization angle. As such, it can be immediately applied to numerous astrophysical situations.