Improving Type Ia Supernova Standard Candle Cosmology Measurements Using Observations of Early-Type Host Galaxies

Type Ia supernovae (SNe Ia) are the current standard-bearers for dark energy but face several hurdles for their continued success in future large surveys. For example, spectroscopic classification of the myriad SNe soon to be discovered will not be possible, and systematics from uncertainties in dust corrections and the evolution of SN demographics and/or empirical calibrations used to standardize SNe Ia must be studied. Through the identification of low-dust host galaxies and through increased understanding of both the SN -- progenitor connections and empirical calibrations, host galaxy information may offer opportunities to improve the cosmological utility of SNe Ia.The first half of this thesis analyzes the sample of SNe~Ia discovered by the Hubble Space Telescope (HST) Cluster Supernova Survey augmented with {\it HST}-observed SNe~Ia in the Great Observatories Origins Deep Survey (GOODS) fields. Correlations between properties of SNe and their host galaxies are examined at high redshift. Using galaxy color and quantitative morphology to determine the red sequence in 25 clusters, a model is developed to distinguish passively evolving early-type galaxies from star-forming galaxies in both clusters and the field. With this approach, 6 early-type cluster member hosts and 11 SN~Ia early-type field hosts are identified. For the first time at z>0.9, the correlation between host galaxy type and the rise and fall time of SN~Ia light curves is confirmed. The relatively simple spectral energy distributions of early-type galaxies also enables stellar mass measurements for these hosts. In combination with literature host mass measurements, these measurements are used to show, at z>0.9, a hint of the correlation between host mass and Hubble residuals reported at lower redshift. By simultaneously fitting cluster galaxy formation histories and dust content to the scatter of the cluster red sequences, it is shown that dust reddening of early-type cluster SN hosts is likely less than E(B-V) < 0.06. Hence, the early-type-hosted SNe~Ia identified here occupy a more favorable environment to use as well-characterized high-redshift standard candles than other SNe Ia.The second half of this thesis analyzes a sample of 40 deep, very high signal-to-noise ratio spectra of nearby SN~Ia host galaxies. These host galaxies are chosen from the Nearby Supernova Factory, the SDSS-II SN Survey, and {\it Swift}-observed SNe, with the requirement that they have passive stellar populations suitable for detailed absorption line measurements. From these spectra, ages and the abundances of multiple elements, including Fe, Mg, C, N, and Ca are derived. The correlation between SN decline rate and host galaxy age is rediscovered at high significance. SN decline rate is also shown to be correlated with host [Fe/H], [C/Fe], and [N/Fe]. In contrast to studies of mixed-host samples, however, no evidence is found supporting a correlation with SN Hubble residuals and host galaxy properties. The wide range in age spanned by the sample, in particular, suggests that age is not responsible for the host-mass -- Hubble residual relation reported in the literature