Non-Gaussian information in Cosmology with Weak Gravitational Lensing

The Standard Model of cosmology successfully describes the observable Universe requiring only a small number of free parameters. The model has been validated by a wide range of observable probes such as Supernovae IA, the CMB, Baryonic Acoustic Oscillations and galaxy clusters. Weak Gravitational Lensing (WL) is becoming a popular observational technique to constrain parameters in the Standard Model and is particularly appealing to the scientific community because the tracers it relies on, image distortions, are unbiased probes of density fluctuations in the fabric of the cosmos. The WL effect is sensitive to the late time evolution of the Universe, in which structures are non--linear. Because of this, WL observations cannot be treated as Gaussian random fields and statistical information on cosmology leaks from quadratic correlations into more complicated, higher order, image features. The goal of this dissertation is to analyze the efficiency of some of these higher order features in constraining Standard Model parameters. We approach the investigation from a practical point of view, examining the analytical, computational and numerical accuracy issues that are involved in carrying a complete analysis from observational data to parameter constraints using these higher order statistics. This work is organized as follows: - In Chapter 1 we review the fundamentals of the LambdaCDM Standard Model of cosmology, focusing particularly on the Friedmann picture and on the physics of large scale density fluctuations. - In Chapter 2 we give an outline of the Gravitational Lensing effect in the context of cosmology, and we introduce the basic WL observables from an analytical point of view. - In Chapter 3 we review the relevant numerical techniques used in the modeling of WL observables, focusing in particular on the algorithms used in ray--tracing simulations. These simulations constitute the base of our modeling efforts. - In Chapter 4 we discuss feature extraction techniques from WL observations: we treat both quadratic statistics, such as the angular shear--shear power spectrum, and higher order statistics for which analytical treatment is not possible. - In Chapter 5 we review the Bayesian formalism behind the inference of LambdaCDM parameters from image features. We place particular emphasis on physical and numerical effects that degrade parameter constraints and discuss possible mitigations. -In Chapter 6 we apply the previously described techniques to the Canada France Hawaii LenS galaxy survey, showing how the use of higher order image statistics can improve inferences on the LambdaCDM parameters that describe density fluctuations. - In Chapter 7 we discuss some of the issues that arise in the analysis of a large scale WL survey such as the Large Scale Synoptic Survey: we focus on systematic effects caused by sensors imperfections, the atmosphere, redshift errors and approximate theoretical modeling. - In Chapter 8 we draw our conclusions and discuss possible future developments.