All-sky radiative transfer and characterisation for cosmic structures

This thesis focuses on providing a solid theoretical foundation and the associated methodologies for the studies of cosmic magnetism and cosmological reionisation. It develops covariant formalisms of cosmological radiative transport of (i) polarised continuum radiation, and (ii) 21-cm line of neutral hydrogen that calculate, from first principles, the polarisation arising from the emergence and evolution of cosmic magnetic fields and the tomographic 21-cm line signals associated with cosmological reionisation, respectively. The two formalisms, namely the cosmological polarised radiative transfer (CPRT) and the cosmological 21-cm line radiative transfer (C21LRT), self-consistently account for the relevant radiation processes, relativistic and cosmological effects along a ray transported in an expanding, evolving Universe. Their all-sky algorithms adopt a ray-tracing method and a post-processing approach by which complex physical models, such as those obtained from cosmological simulations, can be accounted for in the radiative transfer calculations. The power of the CPRT calculations to compute unambiguous point-to-point polarisation of large-scale structures, such as a 3D simulated galaxy cluster and a modelled magnetised universe, is demonstrated. The ability of the C21LRT formulation to calculate the 21-cm line spectra across cosmic time, with full accounts of the essential cosmological radiative transfer effects, is verified. Furthermore, a new spherical curvelet transform for efficient extraction of directional, elongated features within spherical data is constructed. It is particularly useful for the studies in wide-field astronomical research, such as analyses of the data of continuum polarisation and the structured 21-cm line from all-sky surveys or the CPRT and C21LRT calculations. The formulations, methodologies and techniques developed in this work together establish a solid framework within which reliable theoretical predictions and robust data characterisation can be made, ultimately laying a foundation for the meaningful physical interpretation of observations and studying the structural evolution of the magnetic ionised Universe.