A quadratic estimator for the matter power spectrum from weak gravitational lensing

In this thesis a new quadratic estimator for the power spectrum, based on weak lensing measurements, is developed. According to the Cramer-Rao inequality, the estimator is guaranteed to have the minimum variance and is therefore the best unbiased estimator of the power spectrum. The properties of this estimator are explored, in particular its window functions which are optimised to be as narrow as possible in k-space. This would permit to isolate the effects of physical processes that act on different scales. A major goal here is to detect features at k~1 hMp(c^-1) arising from non-zero neutrino masses. A second is to develop statistics that are insensitive to the high-k regime (k > 1 hMp(c^-1)) that may be affected by uncertain baryon feedback processes.