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

TL;DR

This paper derives the second order Boltzmann equation for polarized radiation in cosmology, providing a comprehensive framework without using Stokes parameters, to better understand the polarization effects in the early universe.

Contribution

It presents a novel derivation of the second order Boltzmann equation for polarized radiation using tensor-valued distribution functions, avoiding the traditional Stokes parameters.

Findings

Derived the full second order Boltzmann equation including polarization

Provided a tensor-based formalism for polarized radiation

Enhanced understanding of polarization effects in cosmological perturbations

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.