Abstract: Type Ia supernovae (SNe Ia) are magnificent explosions in the Cosmos that are thought to result from the thermonuclear runaway of white dwarf stars in multistar systems (see, e.g., Jha et al. 2019, for a recent review). Though the exact details of the progenitor system(s) and explosion mechanism(s) remain elusive, SNe Ia have proven themselves to be immensely valuable in shaping our understanding of the physical laws that govern the evolution of the Universe (i.e., physical cosmology). This value is manifested chiefly in two empirical facts: (i) SNe Ia are incredibly luminous (reaching the equivalent of several billion Suns), and (ii) the relatively similar peak luminosities that all "normal" SNe Ia reach can be further homogenized by exploiting a correlation with the rate of photometric evolution (e.g., Phillips 1993). Together, these facts make SNe Ia excellent extragalactic distance indicators, and their use as such led to the discovery of the accelerating expansion of the Universe (Riess et al. 1998; Perlmutter et al. 1999). Through this, the current cosmological paradigm came into favor — the so-called ΛCDM model, where the Universe consists primarily of repulsive dark energy (of which a leading candidate is Einstein’s cosmological constant, Λ) and cold dark matter (CDM).In this thesis, I present a comprehensive study that follows the entire SN Ia cosmology lifecyle, from data acquisition to cosmological analysis (albeit of a different flavor than those mentioned above). While these “bookends” provide natural segmentation points in this thesis, there is a third, intermediate segment which serves to present a complementary method for SN Ia distance measurement that is far less data intensive than conventional approaches. In this way, the segments are hierarchical, each depending on its predecessor and enabling its successor.After appropriately setting the stage in Chapter 1, I delve into the first segment (data acquisition) with Chapter 2, a data release and analysis of 93 multipassband SN Ia light curves collected between 2005 and 2018, and Chapter 3, a complementary release of 637 low-redshift SN Ia optical spectra from a similar time interval. In both, I describe open-source software I developed for data processing and analysis purposes, and make — in addition to the data themselves — useful, value-added data products (e.g., fitted parameters from light curves) available to the community. When combined with prior releases, the Berkeley SN Ia sample now reaches nearly 2000 optical spectra and more than 250 multiband light curves, all observed and processed with the utmost care for quality and internal consistency.This large, homogeneous sample proves critical for the second segment of this thesis, in which I ultimately develop and validate the aforementioned technique — the snapshot distance method (SDM) — for estimating the distance to an SN Ia from sparse observations. As a prerequisite to the SDM, I develop, in Chapter 4, an open-source software package called deepSIP that is capable of determining the phase and light-curve shape of an SN Ia — both of which conventionally require a well-sampled light curve — from a single optical spectrum. At its heart, deepSIP consists of a set of three convolutional neural networks trained on a significant fraction of all publicly available SN Ia optical data (including those presented in the first segment of this thesis), with judicious augmentation steps included to promote telescope agnosticism and model robustness. The impressive performance of deepSIP enables the SDM, which, as I demonstrate in Chapter 5, is capable of deriving an SN Ia distance estimate from as little as one optical spectrum and one epoch of 2+ passband photometry with notable precision over a wide range of SN Ia parameters.This leads, finally, into the last segment of this thesis (cosmological analysis), where I use the SDM to turn trash (i.e., SN Ia observations that were previously unusable owing to data sparsity) into treasure (i.e., reliable distance estimates to be used in a cosmological study). In particular, in Chapter 6, I combine a novel sample of 137 SDM-resurrected SNe Ia with a large literature sample of SNe Ia and SNe II to measure peculiar velocities and set leading (from an SN-only perspective) constraints on the cosmological parameter combination fσ8 and the nature of bulk flows in the local Universe. Moreover, the methods by which I perform this analysis establish a reproducible and extensible blueprint for future such analyses as large-scale surveys come online and unleash an unprecedented data volume.
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