Integrated cosmological probe combination

Abstract

Our Universe is an exciting laboratory, which we can study by observing many of its properties, called cosmological probes. Recent observational progress has led to the establishment of the $\Lambda$CDM cosmological model, which relies on the general theory of relativity, dark matter, dark energy and the existence of primordial perturbations. In spite of this progress, several questions remain unanswered, such as the nature of dark matter and dark energy and the details of the initial conditions. Constraining the key components of the standard model of cosmology is thus one of the main goals of observational cosmology today. In this thesis, we aim to improve our understanding of $\Lambda$CDM by combining the information from different cosmological probes, taking into account both the auto- and the cross-correlations. This allows us to go beyond the notion of isolated probes, towards an integrated view of the Universe and cosmology. In a first step, we compare the constraining power of a future spectroscopic galaxy redshift survey when analyzed using the spherical harmonic tomography power spectrum and the spherical Fourier-Bessel power spectrum in a Fisher matrix analysis. We then develop a framework for integrated analysis of cosmological probes in which the probes are combined starting at the map level. In a first implementation, we apply this framework to a combination of CMB temperature anisotropy measurements from the Planck satellite as well as galaxy clustering and weak lensing measured by the Sloan Digital Sky Survey. We then extend the analysis to also include CMB lensing from Planck, weak lensing from Dark Energy Survey Science Verification data as well as background probes. These analyses yield self-consistent and competitive constraints on cosmological parameters and provide a confirmation of $\Lambda$CDM through the consistency of different probes. As a complement, we quantify possible tensions between these constraints and other existing results through the relative entropy and find all data sets considered to be consistent in the framework of $\Lambda$CDM. Finally, we revisit the relative entropy and propose a novel model selection method, which combines relative entropy and posterior predictive distributions. In a series of toy models and applications to cosmological data, we show that this algorithm gives results consistent with expectations and thus appears promising for model selection in cosmology.