Higher-order statistics in cosmic shear

Abstract

The humble goal of cosmology is to understand the Universe as a whole. In the last decades, the Lambda Cold Dark Matter model has proven itself as the standard model of cosmology by explaining the majority of cosmological observations with remarkable accuracy. However, there is growing evidence that this model will need to be revised: Aside from our inability to explain its main components, in recent years, internal tensions between constraints of the model parameters have emerged. <br /> The weak gravitational lensing effect is one of the best tools to constrain the standard model of cosmology and test potential extensions. It describes the deflection of light from distant galaxies by the tidal gravitational fields of the large-scale structure of the Universe and is an excellent means to study the evolution of structure growth, as it allows us to map the dark matter distribution directly. <br /> In this thesis, I study the use of higher-order statistics to improve the constraining power of weak lensing surveys. I test two higher-order statistics: persistent homology and third-order aperture mass statistics. For the former, we develop a simulation-based inference pipeline to constrain cosmological parameters, show that they perform better than peak count statistics, and conduct a cosmological parameter inference on the year-1 data of the dark energy survey, where we find for the matter clustering parameter $S_8=0.747^{+0.025}_{-0.031}$, which is in full agreement with our analysis of second-order statistics ($S_8=0.759^{+0.049}_{-0.042}$). We further measure a tension in the matter density parameter $Omega_m$, where persistent homology yields $Omega_m = 0.468^{+0.051}_{-0.036}$, in contrast to $Omega_m = 0.256^{+0.034}_{-0.058}$ from the shear two-point correlation functions. <br /> In the second part of this thesis, I present our preparations for a cosmological parameter analysis with third-order aperture mass statistics. We develop and test strategies to model them directly from the matter bispectrum, measure them quickly in simulations, and estimate them from real data. The ability to model these statistics directly gives rise to many validation tests, which we perform to ensure that a subsequent cosmological parameter analysis remains unbiased. Using mock data, we show that a combined analysis of second- and third-order shear statistics of a current-generation survey remains unbiased in the absence of systematics and yields an improvement on the $S_8$-constraints by almost a factor of two, compared to analysis with only second-order statistics. We then develop a model for the covariance of third-order aperture masses and a method to test the individual emerging terms using N-body simulations. <br /> I conclude this thesis by comparing the simulation-based inference method to the direct modelling approach for higher-order shear statistics. I hope our efforts will contribute to testing the standard model of cosmology and its potential extensions with the next generation of weak lensing surveys.