Tracing the Origins: Cosmological Information in the Large-Scale Structure of the Universe

Abstract

One of the central observables in cosmology is the correlation function of the matter density field. Yet, the large-scale structure of the universe cannot be directly observed, as it is dominated by dark matter. To probe it, we rely on indirect tracers such as galaxy surveys, 21-cm observations, gravitational lensing, and the cosmic microwave background. Recent advances in cosmological observations have produced a wealth of data across these tracers, offering unprecedented opportunities to investigate the physical processes and cosmic history that shaped the universe—from its initial conditions to its present state. This data abundance, however, raises two major challenges: (1) How can we efficiently and accurately extract information from the large-scale structure? (2) How can we combine different observational datasets in a consistent joint analysis? Addressing these questions is central to modern cosmological data analysis pipelines. This thesis tackles these challenges through four directions: (1) We apply a novel statistic—the skew-spectrum—to galaxy survey data, enabling efficient compression of the three-point correlation function and improved constraints on primordial non-Gaussianity, a potential signature of inflation. (2) We study the combined information content of galaxy clustering and CMB lensing using both two- and three-point correlation functions. To support this analysis, we develop a new method based on the FFTLog algorithm that significantly accelerates the theoretical computation of projected angular statistics for galaxy surveys and weak lensing. (3) We generalize the skew-spectrum formalism from redshift space to harmonic space, facilitating consistent and efficient cross-correlation studies across different cosmological probes. As a proof of concept, we implement this approach on N-body simulations. (4) We perform field-level inference—applied for the first time to 21-cm signals from the epoch of reionization—within the framework of the effective field theory of large-scale structure. Despite foreground contamination, our high-dimensional Bayesian analysis enables reconstruction of the obscured signal and constraints on key physical parameters. We further explore cutting-edge diffusion-based generative models as an alternative inference method and find that their performance is comparable to traditional approaches.