Weak Gravitational Lensing and Cosmology

Albert Einstein’s General Theory of Relativity radically transformed our understanding of gravitation. Along with this transformative view came several powerful predictions. One of these predictions, the deflection of light in a gravitational field, has proven in recent decades to be crucial to the study of cosmology. In this work we present the foundational theory of gravitational lensing, with a particular focus on the weak regime of lensing. Weak gravitational lensing produced by the large scale structure, called cosmic shear, induces percent level distortions in the images of distant galaxies. Gravitational lensing is of particular interest, since the image distortions are due to all of the matter in the large scale structure, including dark matter. We present the definitions of shear and convergence which are used to quantify the source galaxy image distortions, and discuss some techniques shown in literature which are used for measuring these quantities. This includes presenting the necessary derivations which connect these quantities to two particular classes of results: mass map reconstructions and cosmological parameter constraints. We present some results obtained in recent years: mass map reconstructions obtained using the Canada-France-Hawaii-Telescope Lensing Survey (CFHTLenS) and the Cosmological Evolution Survey (COSMOS), and constraints on the parameters Ω_m and σ_8 (the total matter density parameter and the power spectrum normalization) obtained using CFHTLenS, COSMOS, the Kilo Degree Survey (KiDS), and the Dark Energy Survey (DES). This includes some discussion of apparent tensions with results obtained from Planck (using observations of the cosmic microwave background—a completely different cosmological probe) and of some inconsistencies within the more recent survey results