Cosmology with weak lensing voids and peaks

Abstract

The goal of modern cosmology is to measure cosmological parameters as accurately and precisely as possible, with future stage-IV surveys aiming to achieve this at the
sub-percent level. To maximise the utility of such surveys, we must develop methods that can more fully capture the wealth of cosmological information contained within the data. In this thesis, I develop new weak gravitational lensing statistics as a means to achieve this. To this end, I study in detail the properties of weak lensing voids and peaks. First, I establish weak lensing voids as a new statistic that corresponds to extended underdense regions of convergence maps, and show that they offer several advantages over galaxy voids, including larger lensing profile amplitudes. I then study a range of void finders to test the impact of the void definition on the resulting weak lensing void properties, and identify the tunnel algorithm as the most promising void finder. This is followed by wCDM parameter forecasts from an LSST-like survey for weak lensing voids, which shows that they perform better than the standard shear two-point correlation function. I then show that weak lensing voids also have higher sensitivity to modified gravity theories than galaxy voids. Next, I study the clustering of weak lensing peaks and present simple scaling relations for their two-point correlation function. I then make similar parameter forecasts for the peak two-point correlation function, and show that when combined with the peak abundance, peaks can give tighter constraints than the shear two-point correlation function. Finally, both the void and peak statistics presented in this thesis offer complementary parameter degeneracy directions to the shear two-point correlation function. This makes these statistics invaluable for cosmological parameter measurements from ongoing and future weak lensing surveys.