Cosmological information from moments and Bayesian reconstruction methods

This thesis explores novel ways on constraining the cosmological model of our Universe with observational data. The explosion in high fidelity data coupled with the increasing number of complementary cosmological probes, makes it possible to test our theories to an unprecedented precision. However, reaching the experimental designed precision for the upcoming surveys will require advances in theoretical and statistical modelling. We contribute work to two avenues addressing this problem, in particular by extracting nongaussian information from higher order weak gravitational lensing statistics and by using Bayesian forward modelling approaches to increase the information gain compared to traditional analysis methods. For the first project we focus on the aperture mass statistics, which is a E/B decomposed measure of the weak lensing convergence polyspectra. We construct an accelerated estimator that will make it feasible to measure those statistics in current and forthcoming surveys. After identifying an optimized weighting scheme and adapting the theoretical expressions to account for potential biases, we successfully test the estimators’ performance and reliability on simulated surveys and then measure the second order statistics on the CFHTLenS survey, finding excellent agreement with the traditional analysis in terms of the shear correlation functions. For the second project we move away from summary statistics and shift our focus to the cosmic field itself. Using idealized structure formation models we construct a likelihood function for a linearized cosmic field, taking into account the observed realization of tracers. For an effcient sampling of this high dimensional problem we employ a Hamiltonian Monte Carlo framework. We then extend the likelihood to jointly sample the field and the amplitude of its underlying power spectrum. We find that for realistic scale cuts and galaxy number densities this framework increases the information content by a factor of four.