Alternative estimators for weak gravitational lensing

Weak gravitational lensing provides a means to measure the total mass in the Universe. The incoming light from distant galaxies is disturbed by the inhomogeneity of the dark matter distribution along the line of sight. The correlations of shape in an observed galaxy population can be used to probe the total mass density fluctuations in the Universe. Studies of correlations between galaxy shapes have been the basis of weak lensing research. In this thesis we investigate various non-conventional weak lensing statistics that are complementary to the traditional two-point shear correlation functions. The goal is to constrain the matter density Ωm and normalization of matter power spectrum σ₈ parameters. These higher order statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological parameters. Using ray-tracing simulations, which incorporate important survey features such as a realistic depth-dependent redshift distribution, we find that joint two- and three-point correlation function analysis is a much stronger probe of cosmology than the two-point analysis alone. We apply the higher order statistics technique to the 160 deg² of the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS) and show preliminary results from the joint two- and three-point likelihood analysis. We reveal the possibilities that lie in the projected mass probability distribution function to discriminate models with different values of the matter density parameter. In the process we develop a hybrid data set based on the simulations and the CFHTLenS data for systematics testing and covariance matrix estimations. Our error analysis includes all non-Gaussian terms, finding that the coupling between cosmic variance and shot noise is a non-negligible contribution.Science, Faculty ofPhysics and Astronomy, Department ofGraduat