# Covariant polarized radiative transfer on cosmological scales for investigating large-scale magnetic field structures

## TL;DR

This paper develops a covariant polarized radiative transfer framework for cosmological scales, enabling detailed modeling of polarization signals to study large-scale magnetic fields and aiding future observations like those from SKA.

## Contribution

It introduces a fully covariant CPRT formulation including Faraday effects, and proposes an all-sky ray-tracing algorithm for modeling polarization maps in cosmological simulations.

## Key findings

- Verified the CPRT code with multiple tests.
- Demonstrated applications using galaxy cluster and magnetized universe models.
- Discussed implications for large-scale magnetic field studies.

## Abstract

Polarization of radiation is a powerful tool to study cosmic magnetism and analysis of polarization can be used as a diagnostic tool for large-scale structures. In this paper, we present a solid theoretical foundation for using polarized light to investigate large-scale magnetic field structures: the cosmological polarized radiative transfer (CPRT) formulation. The CPRT formulation is fully covariant. It accounts for cosmological and relativistic effects in a self-consistent manner and explicitly treats Faraday rotation, as well as Faraday conversion, emission, and absorption processes. The formulation is derived from the first principles of conservation of phase-space volume and photon number. Without loss of generality, we consider a flat Friedmann-Robertson-Walker (FRW) space-time metric and construct the corresponding polarized radiative transfer equations. We propose an all-sky CPRT calculation algorithm, based on a ray-tracing method, which allows cosmological simulation results to be incorporated and, thereby, model templates of polarization maps to be constructed. Such maps will be crucial in our interpretation of polarized data, such as those to be collected by the Square Kilometer Array (SKA). We describe several tests which are used for verifying the code and demonstrate applications in the study of the polarization signatures in different distributions of electron number density and magnetic fields. We present a pencil-beam CPRT calculation and an all-sky calculation, using a simulated galaxy cluster or a model magnetized universe obtained from GCMHD+ simulations as the respective input structures. The implications on large-scale magnetic field studies are discussed; remarks on the standard methods using rotation measure are highlighted.