The radiative transfer for polarized radiation at second order in cosmological perturbations

TL;DR

This work provides a complete treatment of polarized radiation at second order in cosmological perturbations by formulating the Boltzmann equation with a tensor-valued distribution function, avoiding reliance on Stokes parameters. It derives the full second-order Liouville operator and collision term, including polarization, within a framework based on metric perturbations in Poisson gauge and tetrad perturbations, and expands the brightness and polarization in PSTF multipoles. The approach yields a pathway to express the equations in Fourier space and to numerically integrate the second-order Boltzmann hierarchy, enabling accurate predictions of the CMB bispectrum that include polarization. It also discusses separating primordial non-Gaussian signals from non-linear evolution in future high-precision CMB data, and notes that circular polarization is not produced at this order in Thomson scattering.

Abstract

This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by using a tensor valued distribution function, the second order Boltzmann equation, including polarization, is derived without relying on the Stokes parameters.