Magnetic fields are of fundamental importance in understanding the Universe, but we have yet to know their origin and evolution in galaxies and the cosmic web. We have even yet to measure the present-day structure of these large-scale magnetic fields.
In this talk, I will present a solid theoretical foundation for using polarised light to investigate large-scale cosmic magnetic fields, namely the cosmological polarised radiative transfer (CPRT) formulation. I will show several demonstrations to illustrate how the CPRT calculations can interface with cosmological MHD simulation results, e.g., GCMHD+, to generate polarisation maps of astrophysical objects (using a simulated galaxy cluster) and the entire polarized radio sky (using a modelled magnetic universe). Such maps will be crucial in our interpretation of polarisation data, such as those to be collected by the Square Kilometer Array (SKA). I will also discuss assessing the physical basis of standard magnetic-field diagnostics — Faraday rotation measure (RM) and RM fluctuations — under the CPRT framework.