Bayesian methods in a flexible universe: sampling, tension and dark energy

Abstract

Chapter 0 begins with an overview of the cosmology background to this thesis. It also provides an introduction to Bayesian methods and nested sampling, and the challenges of multi-modal problems. Chapter 1 contains the work of Ormondroyd et al. (2023b), which demonstrates the effect of informative priors on parameter estimation in the context of Cosmic Microwave Background lensing. It also introduces dataset tension analysis, which is used extensively in the subsequent three chapters. Chapters 2, 3 and 4 were published in Ormondroyd et al. (2025c,a,b). Chapter 2 performs a free-form reconstruction of the history of the dark energy equation of state, using Baryon Acoustic Oscillations and Type Ia supernovae. Evidence is found for an evolving equation of state. Chapter 3 updates these conclusions in light of new data, then Chapter 4 finds that there is more evidence for a systematic issue with low-redshift supernovae. Chapter 5 focusses on the performance of different clustering approaches for mode detection in nested sampling, to address an issue found with a reconstruction of the primordial curvature perturbation power spectrum using CMB anisotropies. Algorithms which make use of likelihood information are found to be robust for this application. Chapter 6 investigates volume correlations of ergodically-separated prior regions during nested sampling. This sought to address the "Polya's urn" feedback loop of multi-modal sampling. Chapter 7 concludes this thesis and provides suggestions for future research.