
Type Ia supernovae (SNe Ia) have been instrumental in arriving at our current understanding of the Universe, from first indicating its accelerated expansion in the late 1990s, to now continuing to improve cosmological constraints. In particular, SNe Ia are a powerful probe for the quantities that parametrise LambdaCDM, and the equationofstate parameter w for dark energy. The paradigm for cosmology is now to diminish systematic errors to obtain precise measurements, while making observations further into the past to measure dark energy. More locally, the Hubble constant H_0 determines the expansion rate of the Universe at present, normalising its distance scale. In the past several years, the precise value of H_0 has come into contention, with a significant discrepancy between results determined from a local distance ladder, and those inferred from observations of the early Universe. Taken at face value, this discrepancy could signal systematic errors in either measurement, or inaccurate assumptions about the model. I will discuss these questions at both ends of the Universe’s expansion history. In the works in my thesis, I have developed a framework for performing precise cosmological analyses of SN Ia samples, utilising current best methods to account for the statistical and systematic uncertainties by using full covariance matrices, combined with probabilistic Bayesian methods to estimate cosmological parameters and uncertainties. I have applied these methods to supernova data in SH0ES (Riess et al. 2011) and the Dark Energy Survey to address the tension in the Hubble constant locally, and the nature of dark energy at higher redshifts. 
