In Part I we introduce the method and results of the Twin Supernova analysis.

This novel approach to Type Ia supernova standardization is currently only possible with

spectrophotometric timeseries observations from the Nearby Supernova Factory. As Chapters

1 through 4 will explore, we select an ideal subset of supernovae, find pairs whose features

match well in flux at all wavelengths and times, and test their dispersion in brightness.

The analysis is completed in a blinded fashion, ensuring that we are not tuning our results.

What we find is that twin supernovae do indeed have a small brightness dispersion.

Part II shows two additional analyses related to the standardization of Type Ia supernovae.

In Chapter 5 we present a check on the results of Bailey et al. [2009]. Literature supernovae

with spectra near maximum light were tested to see how well their magnitudes could be standardized

using the flux ratio method of Bailey et al [2009].

Chapter 6 shows a study with data from the Nearby Supernova Factory. Using only the

spectrophotometric observations near maximum light, we calculate monochromatic Hubble Diagram

residuals for each supernova. Those residuals are then corrected using a flux ratio, similar

to Bailey et al. [2009] to test the standardization possibilities using only near-maximum observations.

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.

Type Ia Supernovae provided the first strong evidence of dark energy and are still an important tool for measuring the accelerated expansion of the universe. However, future improvements will be limited by systematic uncertainties in our use of Type Ia supernovae as standard candles. Using Type Ia supernovae for cosmology relies on our ability to standardize their absolute magnitudes, but this relies on imperfect models of supernova spectra time series. This thesis is focused on using data from the Nearby Supernova Factory both to understand current sources of uncertainty in standardizing Type Ia supernovae and to develop techniques that can be used to limit uncertainty in future analyses.

Part I of this thesis is concerned with studying systematic errors that occur in the current generation of supernova lightcurve models. Lightcurve models are used to fit photometric supernova data, generating a small number of parameters that can then be used to `correct' the supernova magnitude to a standard value. The analysis presented here estimates systematic errors due to K-corrections that occur when using such lightcurve models to fit high-redshift supernovae. These errors occur when the spectral template underlying the lightcurve fitter poorly matches the actual supernova spectral energy distribution and also if the model fit is dependent on the spectral coverage of the photometric filters used to observe the supernova.

In order to quantify this effect, synthetic photometry is performed on artificially redshifted spectrophotometric data from the Nearby Supernova Factory, simulating having photometric data for the same supernovae with a range of filter positions. The resulting lightcurves are fit with a conventional lightcurve fitter and the variation is measured in the resulting standardized magnitudes. We find significant variation in the measurements of the same supernovae placed at different redshifts regardless of filters used, which causes dispersion greater than $\sim 0.05$ mag for measurements of photometry using Sloan-like filters and a bias that corresponds to a 0.03 shift in $w$ when applied to an outside data set. We also test the effect of population changes at high redshift and measure the resulting bias for the average of the supernova magnitudes. Lastly, methods are discussed for mitigating bias and dispersion due to K-corrections.

Part II presents an alternative to current lightcurve models. The supernovae from the Nearby Supernova Factory are used to develop an empirical model that will be able to more fully describe the variety of supernova behavior. The spectrophotometric time series for over 200 supernova are used to fit linear principal components that will be able to be used as a lightcurve model. This is done by first using Gaussian Processes to model the true spectral time series for each supernova and make a prediction for it on a regular grid in time and wavelength space. Once this has been done, principal components are calculated that describe the full set of supernovae using a method that incorporates the variance in the data. K-fold cross-validation is used to determine how many components best describe the full population without over-training on noise in the data. In the final version of the analysis, three different models are presented: one simple model that can be compared to the current generation of lightcurve models; one model that is the best for performing a linear standardization of supernova magnitudes following current standardization methods, at least when spectra for the supernova are available; and one complex model that provides the most complete model of spectral time series for the full population.

This dissertation chronicles the development of the "Union" SN Ia analyses. These analyses address the challenges of supernova cosmology with uniform treatment of light-curve fitting, selection cuts, and outlier rejection. They were the first analyses to propagate systematic uncertainties into a covariance matrix, allowing constraints including systematics to be computed for any cosmological model. To minimize unintentional biases towards the concordance cosmology, each analysis was developed with the cosmology hidden ("blinded"). With each Union compilation version, we combine with BAO and CMB constraints to compute the then-best constraints on dark energy.

Chapter 2 provides the basic analysis outline that remains in place for subsequent compilations. Using the resulting compilation of 307 SNe (after cuts), we combine with BAO and CMB data and find that the equation of state parameter w is constrained to be -0.969^{+0.059}_{-0.063} (statistical uncertainties only) ^{+0.086}_{-0.091} (with systematics) for a flat universe with constant w. For non-constant w, no real constraints (σ_w ~1) are possible above redshift 0.5.

Chapter 3 follows our application of the Union compilation to a range of dynamical dark energy models. We find that many classes of physical models are indistinguishable from LambdaCDM with the current level of data.

In Chapter 4, we present an update of the Union compilation framework, with improved light-curve fitting and an improved treatment of systematic uncertainties. This new compilation, now consisting of 557 supernovae, gives constraints of w = -0.997^{+0.050}_{-0.054} (statistical) ^{+0.077}_{-0.082} (with systematics) when combined with BAO and CMB data.

Chapter 5 outlines supernova discoveries from the HST Cluster Supernova Survey, with 14 cosmologically useful high-redshift SNe passing Union selection cuts. We present the photometry of the undersampled IR images, accomplished by directly modeling the pixels as observed. The photometry quality approaches photon-limited statistics. We also update the Union compilation to remove the effect of host-galaxy environment on corrected supernova distances. Using our updated compilation of 580 SNe, with BAO, CMB, and H_0 measurements, we find a constraint on the equation of state parameter of w = -1.008^{+0.050}_{-0.054} (statistical) or -1.013^{+0.068}_{-0.073} (with systematics).

Chapter 6 presents the analysis of a SN discovered in an SCP search of GOODS that did not have a firm redshift at the time of discovery. An archival WFC3 IR spectrum enabled us to get the redshift of the likely host galaxy. With this redshift in hand, we used a novel PCA-like classification to confirm the supernova as a Ia with 92\% confidence. At z=1.713, this was until recently the highest-redshift SN Ia with spectroscopic confirmation, and it remains the highest one with a precision color measurement. Although limited by our sample size of one, we see no evidence of population evolution.

Finally, Chapter 7 concludes with proposed Bayesian improvements that will yield even better cosmological constraints.

In the late 1990s, precise distance measurements with Type Ia supernovae (SNe Ia) were used to show that the expansion of the universe is accelerating. One possibility is that this accelerated expansion is due to an additional form of energy referred to as “dark energy” which contributes roughly 70% of the total energy in the present day universe. The properties of dark energy are not currently well-constrained, and a wide range of different cosmological probes are currently being designed to explore the fundamental nature of the accelerated expansion of the universe. SNe Ia have remained one of the strongest cosmological probes, and upcoming experiments such as the Large Synoptic Survey Telescope (LSST) are expected to discover over 100,000 SNe Ia that can be used for cosmology. The uncertainties on cosmological parameters derived from these large samples of SNe Ia will be entirely dominated by the systematic uncertainties of distance measurements to SNe Ia. In this dissertation, we discuss several different methods of improving the systematic uncertainties in distance measurements to SNe Ia.

This dissertation is split into three main chapters each discussing how to improve a different aspect of distance measurements to SNe Ia. In Chapter 2, we examine how instrumental calibration can affect these distance measurements, and discuss a new anomalous behaviour of CCD readout electronics related to the binary encoding of pixel values that affects most astronomical instruments currently in use. For the Nearby Supernova Factory, this anomaly introduces a dispersion in the measured B-band/U-band magnitudes of 0.11 mag/0.51 mag for the faintest 20% of measurements.

Another major source of systematic uncertainty in distance measurements to SNe Ia is intrinsic variation of the SNe Ia. In Chapter 3, we develop a new method of parametrizing SNe Ia using manifold learning to generate a non-linear decomposition of the intrinsic diversity of their spectra near maximum light. We identify regions of the parameter space of SNe Ia where previous standardization methods such as SALT2 have biases of up to 0.3 mag, and show how correlations between host galaxy properties and distance estimates are greatly reduced when standardizing SNe Ia using our new parametrization.

Finally, in Chapter 4, we discuss how upcoming surveys such as LSST will need to rely on photometric classification to identify the majority of the transients that they discover, which means that samples of SNe Ia used for cosmology will be contaminated with other types of transients. We developed a set of techniques for photometric classification to address the fact that spectroscopic subsamples used for training classifiers are typically highly biased compared to the full samples of transients and variables that will be discovered. Using these techniques, we built a photometric classifier that won the PLAsTiCC photometric classification challenge out of 1,094 competing teams.

Type Ia supernovae (SNe Ia) remain one of the best astronomical tools available for measuring large distances. Observations of SNe Ia were instrumental in the discovery of the accelerating expansion of the universe, and will be key to understanding the nature of the "dark energy" driving this accelerating expansion. Surveys like LSST and the Roman Space Telescope supernova survey are currently being designed to discover and follow a large number of SNe Ia -- a large enough number that the statistical error will be far subdominant to the systematic error. In order to avoid biases in the cosmological parameters constrained by these future surveys, it is essential that we understand the sources and effects of systematic uncertainties. This dissertation addresses some of these systematic biases.

In Chapter 2, we present two measurements of the extent of charge transfer inefficiency (CTI) in the detectors of the SNIFS instrument that was used to collect much of the data used throughout this dissertation. If the inefficiency is too high in spectroscopic instruments like SNIFS, the smearing that CTI causes can lead to misinterpretation of the resulting spectra. We find that the CTI is low in all detectors (about 1 photoelectron in every million is trapped), and that the low CTI remains stable over time.

Chapter 3 focuses on modeling a particular spectral region of Type Ia supernova spectra near maximum brightness. This region of the spectrum is used in some subclassification schemes of SNe Ia, and can also serve as a proxy for identifying changes in the populations of these subtypes with redshift. Our model can provide accurate measurements of ejecta velocities and the feature equivalent width using low-resolution and/or noisy spectra. Being able to use lower-quality spectra allows us to mitigate bias out to earlier eras of cosmic history by allowing us to monitor population drifts at higher redshifts.

In Chapter 4, we study two empirical models of Type Ia supernova spectral evolution (SALT2 and SNEMO) and measure how well they can capture a variety of near-maximum spectroscopic features. Our goal is to analyse how linear spectral models with differing number of parameters can capture non-linear features like ejecta velocities. In addition, we present a model for producing realistic mock spectra based on these models, allowing future studies to have access to spectral templates that capture the full range of supernova spectral behavior.

Chapter 5 centers on an assumption of linear regression that is often overlooked in supernova cosmology analyses. These analyses perform an initial linear regression to correct the observed SN absolute magnitudes for other properties of the SN. They then perform a second regression to correct the residuals of this first regression for an additional covariate. This practice is statistically sound only if the covariates in the initial regression are not correlated with the covariates used in the second regression. However, these correlations do exist. We present a toy model of this problem to calculate closed-form expressions and scaling relations of the size of the biases in the effect sizes and estimated scatter that come from this overlooked assumption. We also use simulations based on literature data to calculate the size of these biases and provide potential corrections.

Chapter 6 presents two new models of Type Ia supernova spectroscopy that were constructed using deep learning. These models extend the "twins embedding" model of Boone et al. (submitted) into a wide range of phases. The spec2embed model takes as input a spectrum observed at any phase from -10 to +40 days after maximum brightness, and predicts the spectrum's phase and its supernova's location in the twins embedding space. Using these predictions, we can standardize supernovae from single spectra with comparable precision to the original twins embedding work. The embed2spec model works in reverse, taking a phase (or range of phases) and location in the twins embedding space to predict a spectrum. With this, we can use forward-modeling fitting techniques to constrain a supernova's location in the twins embedding space from multiple spectra, spectra with lower spectral resolution, or even broadband photometry.

This thesis presents Type Ia supernova (SN Ia) rates from the Hubble Space Telescope (HST) Cluster Supernova Survey, a program designed to efficiently detect and observe high-redshift supernovae by targeting massive galaxy clusters at redshifts 0.9 < z < 1.46. Among other uses, measurements of the rate at which SNe Ia occur can be used to help constrain the SN Ia ``progenitor scenario.'' The progenitor scenario, the process that leads to a SN~Ia, is a particularly poorly understood aspect of these events. Fortunately, the progenitor is directly linked to the delay time between star formation and supernova explosion. Supernova rates can be used to measure the distribution of these delay times and thus yield information about the elusive progenitors.

Galaxy clusters, with their simpler star formation histories, offer an ideal environment for measuring the delay time distribution. In this thesis the SN Ia rate in clusters is calculated based on 8 +/- 1 cluster SNe Ia discovered in the HST Cluster Supernova Survey. This is the first cluster SN Ia rate measurement with detected z<\italic> > 0.9 SNe. The SN Ia rate is found to be 0.50^+0.23_-0.19 (stat) ^+0.10_-0.09 (sys) h₇₀² SNuB (SNuB = 10^-12 SNe L_sun,B^-1 yr^-1), or in units of stellar mass, 0.36^+0.16_-0.13 (stat) ^+0.07_-0.06 (sys) h₇₀² SNuM (SNuM = 10^-12 SNe M_sun^-1 yr^-1). This represents a factor of approximately 5 +/- 2 increase over measurements of the cluster rate at z < 0.2 and is the first significant detection of a changing cluster SN Ia rate with redshift. Parameterizing the late-time SN Ia delay time distribution with a power law in time with index s, this measurement in combination with lower-redshift cluster SN Ia rates constrains s = -1.41^+0.47_-0.40, under the approximation of a single-burst cluster formation redshift of z_f = 3. This is generally consistent with expectations for the ``double degenerate'' progenitor scenario and inconsistent with some models for the ``single degenerate'' progenitor scenario predicting a steeper delay time distribution at large delay times. To check for environmental dependence and the influence of younger stellar populations the rate is also calculated specifically in cluster red-sequence galaxies and in morphologically early-type galaxies, with results similar to the full cluster rate. Finally, the upper limit of one host-less cluster SN Ia detected in the survey implies that the fraction of stars in the intra-cluster medium is less than 0.47 (95% confidence), consistent with measurements at lower redshifts.

The volumetric SN Ia rate can also be used to constrain the SN Ia delay time distribution. However, there have been discrepancies in recent analyses of both the high-redshift rate and its implications for the delay time distribution. Here, the volumetric SN Ia rate out to z ∼ 1.6 is measured, based on ∼12 SNe Ia in the foregrounds and backgrounds of the clusters targeted in the survey. The rate is measured in four broad redshift bins. The results are consistent with previous measurements at z > 1 and strengthen the case for a SN Ia rate that is greater than approximately 0.6 × 10^-4 h₇₀³ yr^-1 Mpc^-3 at z ∼ 1 and flattening out at higher redshift. Assumptions about host-galaxy dust extinction used in different high-redshift rate measurements are examined. Different assumptions may account for some of the difference in published results for the z ∼ 1 rate.

The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the universe using the baryon acoustic oscillations technique. The spec- tra of 35 million galaxies and quasars over 14,000 square degrees will be measured during a 5-year survey. A new prime focus corrector for the Mayall telescope at Kitt Peak National Observatory will deliver light to 5,000 individually targeted fiber-fed robotic positioners. The fibers in turn feed ten broadband multi-object spectrographs. This thesis details origi- nal work done in support of the DESI experiment, both for the instrument and survey design and optimization. First, I describe a novel approach for connecting optical fibers using fusion splicing, a method that will be implemented on DESI. Then, I will describe the ProtoDESI experiment, an on-sky technology demonstration with the goal to reduce technical risks asso- ciated with aligning optical fibers with targets using robotic fiber positioners and maintaining the stability required to operate DESI. The ProtoDESI prime focus instrument, which was installed and commissioned on the 4-m Mayall telescope from 2016 August 14 to September 30, consisted of three fiber positioners, illuminated fiducials, and a guide camera. ProtoDESI was successful in acquiring targets with the robotically positioned fibers and demonstrated that the DESI guiding requirements can be met. Finally, I will describe a predictive sky background model for DESI, which is built on the spectra from the 5-year Baryon Oscilla- tion Spectroscopic Survey (BOSS). This dataset consists of ∼1 million unique sky spectra covering 360 - 1040 nm collected in a variety of observational conditions. We measure an inter-airglow line continuum value of ∼ 0.81×10−17erg/cm2/s/ ̊A/arcsec2 in dark time across the full wavelength range, with a variance of ∼ 0.175 × 10−17erg/cm2/s/ ̊A/arcsec2. The de- tailed model, which accounts for 50% of the variance, shows that the dark sky continuum consists of ∼ 30% zodiacal light and is significantly impacted by solar activity. The improved spectroscopic sky background model can be used in simulations and forecasting for DESI and other surveys.