Anson D’Aloisio

The statistics of cosmological structures and their associated gravitational lensing effects depend on the initial state of the Universe and the way that it expanded and cooled. Future observational probes of these phenomena are among the most promising ways to gain insight into the fundamental questions of modern Cosmology. The development of a solid theoretical understanding is paramount to the success of future observational efforts. I present progress towards this goal on a number of specific topics in structure formation and gravitational lensing.

Part one of this dissertation utilizes a semi-analytic model to quantify the expected sizes and volume filling fractions of voids in the high-redshift galaxy distribution in the concordance cosmological model. A simple analytic argument is also used to determine the impact of low galaxy densities on high-redshift void measurements. These results are of interest for future galaxy surveys aiming to probe the large-scale structure of the Universe at early times.

The second part of this dissertation explores a topic related to the detection of galaxy clusters with weak gravitational lensing. Some cluster-like weak lensing detections reported in the literature appear to have no optical or X-ray counterpart. We develop a model to investigate a previous claim that unvirialized proto-clusters account for a significant number of these “dark” lenses. We find that the expected number density of proto-clusters that are massive enough to create a weak lensing signal, but under-luminous enough to escape X-ray detection, is too low to be a plausible candidate for dark lenses.

Part three of this dissertation is on the subject of constraining dark energy with strong gravitational lensing in galaxy clusters. The cores of massive galaxy clusters have surface densities that are typically much larger than the critical surface density for strong lensing. As a result, the inner regions of clusters often contain several multiply-imaged background galaxies at different redshifts. These image locations place stringent constraints on central mass distributions and can be used to probe cosmological parameters due to their dependence on the angular diameter distances. We develop numerical simulations to quantify some of the key sources of noise in the technique: the effects of line-of-sight structure and scatter in the cluster galaxy population. We also illustrate that a methodology involving an ensemble of cluster lenses can be used to reduce systematic errors.

The last part of this dissertation investigates the impact of primordial non-Gaussianity on giant-arc statistics. The formation of giant arcs by strong gravitational lensing is reserved for the most massive collapsed structures whose properties are sensitive to the statistics of the initial density fluctuations seeded by inflation. Some types of inflationary models predict deviations from Gaussianity in the initial distribution of fluctuations that are detectable by future observational probes. We first develop a model for quantifying the effects of non-Gaussian initial conditions on the central densities of galaxy clusters. We then calculate how the combined modifications to the central densities of clusters and their abundance alters the predicted probability of giant arc formation.