Advanced gravitational lensing techniques for precision cosmology

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Gravitational lensing - the deflection of light by gravity - has greatly developed since its famous first observation in 1919, which validated Einstein's General Theory of Relativity. The strength of this effect does not depend on the nature of the mass which produces the gravitational field and thus it is a great tool to weigh both the visible and the invisible parts of the universe. Consequently gravitational lensing has become a pillar of observational cosmology over the last decades, and it is used to study the nature of Dark Matter and Dark Energy, the two mysterious quantities which dominate our universe, but are not yet understood by physics theory. The success of this endeavor rests on a thorough understanding of lensing theory and observations, including their systematics, the availability of a sufficient amount of precise data, and the development of efficient software to precisely measure these lensing effects in digital astronomical images. This thesis presents advanced techniques which can improve several of these areas. In the first part, we develop a new theoretical method to break the mass-sheet degeneracy, which prevents accurate mass determinations from lensing observations. The second part focuses on spectroscopic data from MUSE, a second-generation Integral-Field Spectrograph installed on one of the largest ground-based telescopes on earth. We present a pipeline which permits the efficient determination of the redshift of a source observed by MUSE. The redshift indicates the distance of the source from us and depends on the expansion of the universe. In addition, we use MUSE observations of a galaxy cluster to improve the determination of its total weight, including the dominant Dark Matter component. In the third part of this thesis, we investigate how we can accelerate the computation of these mass maps. In the era of big data and large surveys, computing efficiency is key to obtaining new scientific insights. We use High Performance Computing techniques like graphics card acceleration to improve the code performance and we develop a method which harnesses extra performance from using single precision without loosing the required accuracy. In the last section, we present first results from measuring flexion, a higher order lensing effect which could substantially increase the resolution of lensing mass maps and thus lead to a sharper view of structure in the universe.