Two of the fundamental components of the Universe are still poorly understood: dark energy and dark matter. Collectively, these constitute around 95% of the Universe according to our current best measurements. This stresses the need to accurately model them. A particularly powerful probe of these quantities is the effect of weak gravitational lensing. This is the distortion of images of distant galaxies due to the gravitational effects of the large-scale structure of the Universe.
Upcoming weak lensing surveys, known as Stage IV experiments, are poised for more than an order-of-magnitude improvement in cosmological parameter constraining ability. Accordingly, it is paramount that the accuracy of our theoretical models keeps in step. In this thesis, I examine four previously neglected systematic effects, and report on their importance for upcoming experiments, particularly focusing on the most imminent of the Stage IV surveys, the Euclid}space telescope. I also discuss a potential mitigation strategy for them.
Within this work, I first examine the impact of the reduced shear approximation and magnification bias. Specifically, I evaluate the biases in cosmological inference from neglecting these effects. For these terms, assuming a w0waCDM cosmology, I find significant biases in Ωm, σ8, ns, ΩDE, w0, and wa. I then describe how these two corrections depend on another common approximation; the Limber approximation. I find that the Limber approximation can be safely used when evaluating the reduced shear and magnification bias corrections for Stage IV. Another neglected effect I study is the Doppler-shift of galaxies towards their local over-density. I again find this effect is not significant for a Euclid-like experiment. Finally, I report on how a scale-cutting technique, k-cut cosmic shear, can be used to bypass the need for these corrections, without significantly weakening cosmological constraints
