High precision modeling of polarized signals: moment expansion method
  generalized to spin-2 fields
  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 parameter 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 SED
distortions and polarization mixing. Additional dependencies are introduced at
higher order, and we demonstrate on several illustrative examples how these can
be accounted for. Our new modeling of the polarized SED 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.
