|Institution:||University of Cape Town|
|Full text PDF:||http://hdl.handle.net/11427/20770|
A fundamental issue in modern science is the dark energy problem - the apparent accelerating expansion of the universe. Many cosmological observations of the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillation (BAO) and weak lensing have been carried out to try to understand the nature of this repulsive dark force. With the advent of advanced experiments like the Square Kilometer Array we enter the era of precision cosmology where measurements of effects such as weak lensing will be achieved at a sub percent level, implying strong constraints on dark energy. The full picture of weak lensing includes linear and non-linear correction terms to its standard formula. In this thesis we address the questions: Are some of these effects detectable? Under which conditions can we safely neglect them such that the analysis of future weak lensing observations is not biased? Induced by gravity, peculiar velocity of galaxies can potentially be used to probe the growth of structure in our universe. Peculiar velocities induce a lensing-like effect, which we consider as Doppler magnification. By developing new statistical tools which are based on Doppler magnification, we investigate the dark energy problem. These new statistical probes also enable us to explore the viability of other theories that attempt to account for the apparent acceleration of the cosmic expansion by modifying Einstein's General Relativity. Advisors/Committee Members: Clarkson, Chris (advisor).