The Dark Energy Spectroscopic Instrument (DESI) will soon start to obtain optical spectra for tens of millions of galaxies and quasars, constructing a 3-dimensional map spanning the nearby universe to 10 billion light-years. DESI aims to use the fossil imprint of sound waves from the first 380,000 years of the universe, which is still detectable as a pattern of temperature variations in the cosmic microwave background radiation (CMB), to measure how the universe has evolved since then the Baryon Acoustic Oscillations (BAO) technique. The early CMB temperature differences map early variations in density (the sound waves) that subsequently evolved into the clustering of galaxies and intergalactic gas (the baryons), as well as dark matter at recurrent intervals throughout space. These regularly spaced clusterings are consistent over time, very much like a ruler to measure the universe, with the CMB at one end. This allows one to measure the effect of dark energy on the expansion of the universe.

This thesis presents my work as a member of the DESI Imaging Team, for which I received DESI Builder status. We transform images of the night sky into a catalog of positions properties of automatically detected and measured astrophysical sources. This catalog will contain billions of astrophysical sources, but just a subset (tens of millions) of sources will be selected for spectroscopic observation with DESI. I was involved in all stages of the Legacy Surveys, from carrying out observations to building the large–scale-structure catalogs.

A major challenge for they Legacy Surveys is understanding the inevitable biases and systematics in their galaxy samples. The key product of my thesis is a Monte Carlo method, called Obiwan, that adds simulated sources to random locations in astronomical images and then performs source detection and measurement, characterizing the complex selection inherent in large-scale-structure catalogs. The process is repeated until the injected source density is high enough to satisfy one’s science objectives. For instance, the DESI target density for emission line galaxies (ELGs) is 2400 deg2, so simulated ELGs should be injected at more than 10 times this density.

The Intergalactic Medium (IGM) is the dominant reservoir of matter in the Universe from which the cosmic web and galaxies form. The structure and physical state of the IGM provides insight into the cosmological model of the Universe, the origin and timeline of the reionization of the Universe, as well as being an essential ingredient in our understanding of galaxy formation and evolution. Our primary handle on this information is a signal known as the Lyman-alpha forest (or Ly-alpha forest) -- the collection of absorption features in high-redshift sources due to intervening neutral hydrogen, which scatters HI Ly-alpha photons out of the line of sight. The Ly-alpha forest flux traces density fluctuations at high redshift and at moderate overdensities, making it an excellent tool for mapping large-scale structure and constraining cosmological parameters. Although the computational methodology for simulating the Ly-alpha forest has existed for over a decade, we are just now approaching the scale of computing power required to simultaneously capture large cosmological scales and the scales of the smallest absorption systems. My thesis focuses on using simulations at the edge of modern computing to produce precise predictions of the statistics of the Ly-alpha forest and to better understand the structure of the IGM.

In the first part of my thesis, I review the state of hydrodynamic simulations of the IGM, including pitfalls of the existing under-resolved simulations. Our group developed a new cosmological hydrodynamics code to tackle the computational challenge, and I developed a distributed analysis framework to compute flux statistics from our simulations. I present flux statistics derived from a suite of our large hydrodynamic simulations and demonstrate convergence to the per cent level. I also compare flux statistics derived from simulations using different discretizations and hydrodynamic schemes (Eulerian finite volume vs. smoothed particle hydrodynamics) and discuss differences in their convergence behavior, their overall agreement, and the implications for cosmological constraints.

In the second part of my thesis, I present a tomographic reconstruction method that allows us to make 3D maps of the IGM with Mpc resolution. In order to make reconstructions of large surveys computationally feasible, I developed a new Wiener Filter application with an algorithm specialized to our problem, which significantly reduces the space and time complexity compared to previous implementations. I explore two scientific applications of the maps: finding protoclusters by searching the maps for large, contiguous regions of low flux and finding cosmic voids by searching the maps for regions of high flux. Using a large N-body simulation, I identify and characterize both protoclusters and voids at z = 2.5, in the middle of the redshift range being mapped by ongoing surveys. I provide simple methods for identifying protocluster and void candidates in the tomographic flux maps, and then test them on mock surveys and reconstructions. I present forecasts for sample purity and completeness and other scientific applications of these large, high-redshift objects.

This dissertation presents solutions to some problems associated with using strongly gravitationally lensed supernovae (gLSNe) to measure the cosmological parameters. Chief among these are new methods for finding gLSNe and extracting their time delays in the presence of microlensing. The first of these results increased the expected gLSN yields of the Zwicky Transient Facility and the Large Synoptic Survey Telescope, upcoming wide-field optical imaging surveys, by an order of magnitude. The latter of these results involved performing simulations of radiation transport in supernova atmospheres. These simulations provided evidence that some Type Ia supernovae come from sub-Chandrasekhar mass progenitors.

Because of their intrinsic brightness, supernovae make excellent cosmological probes. We describe the spectral-fitting expanding atmosphere method (SEAM) for obtaining distances to Type IIP supernovae (SNe IIP) and present a distance to SN 1999em for which a Cepheid distance exists. Our models give results consistent with the Cepheid distance, even though we have not attempted to tune the underlying hydrodynamical model but have simply chosen the best fits. This is in contradistinction to the expanding photosphere method (EPM), which yields a distance to SN 1999em that is 50 percent smaller than the Cepheid distance. We emphasize the differences between the SEAM and the EPM. We show that the dilution factors used in the EPM analysis were systematically too small at later epochs. We also show that the EPM blackbody assumption is suspect. Since SNe IIP are visible to redshifts as high as z<~;6, with the James Webb Space Telescope, the SEAM may be a valuable probe of the early universe.

Though fundamental to our understanding of stellar, galactic, and cosmic evolution, the stellar explosions known as supernovae (SNe) remain mysterious. We know that mass loss and mass transfer are central processes in the evolution of a star to the supernova event, particularly for thermonuclear Type Ia supernovae (SNe Ia), which are in a close binary system. The circumstellar environment (CSE) contains a record of the mass lost from the progenitor system in the centuries prior to explosion and is therefore a key diagnostic of SN progenitors. Unfortunately, tools for studying the CSE are specialized to stellar winds rather than the more complicated and violent mass-loss processes hypothesized for SN Ia progenitors.

This thesis presents models for constraining the properties of a CSE detached from the stellar surface. In such cases, the circumstellar material (CSM) may not be observed until interaction occurs and dominates the SN light weeks or even months after maximum light. I suggest we call SNe with delayed interaction SNe X;n (i.e. SNe Ia;n, SNe Ib;n). I per- formed numerical hydrodynamic simulations and radiation transport calculations to study the evolution of shocks in these systems. I distilled these results into simple equations that translate radio luminosity into a physical description of the CSE. I applied my straightfor- ward procedure to derive upper limits on the CSM for three SNe Ia: SN 2011fe, SN 2014J, and SN 2015cp. I modeled interaction to late times for the SN Ia;n PTF11kx; this led to my participation in the program that discovered interaction in SN 2015cp. Finally, I ex- panded my simulations to study the Type Ib;n SN 2014C, the first optically-confirmed SN X;n with a radio detection. My SN 2014C models represent the first time an SN X;n has been simultaneous modeled in the x-ray and radio wavelengths.