Third-order Cosmic Shear Statistics

Abstract

Weak gravitational lensing has emerged in the last decade as a competitive cosmological probe to observationally constrain the properties of dark energy, probably the one with the most statistical power when the results of forthcoming large-field imaging surveys are available. In this thesis we investigate weak lensing third-order statistics, a statistical tool which will be applied to future surveys to further enhance the power of weak lensing. Our investigations center on three aspects of weak lensing third-order statistics, namely how the observable shear can be related to theoretical predictions of the matter density field, how much information third-order statistics can provide, and how systematical errors can be controlled. A rigorous derivation of the form of bispectrum covariance is given. The nulling technique, a method to control the intrinsic-shear alignment systematics, has been generalized to the third-order statistics. The relations between third-order shear observables and the configuration space statistics of the underlying matter density field are established, and conditions for E/B-mode decomposition are found for third-order shear statistics.