Woldesenbet, Addishiwot2016-09-192016-09-192015-04https://hdl.handle.net/11299/182230University of Minnesota Ph.D. dissertation. April 2015. Major: Physics. Advisor: Liliya Williams. 1 computer file (PDF); x, 135 pages.Gravitational lensing has proven to be a very valuable tool as a probe to better understand our universe. Parametric modeling of one multiple image gravitational lens system at a time is a common practice in the field of lensing. Instead of individual lens modeling, an alternative approach is to use symmetries in different spaces to make conclusions about families of lenses. The latter method is the focus of this thesis. Three types of lenses are defined based on whether they do or do not obey two-fold and double mirror symmetries. The analysis concentrates on quadruply imaged systems, or quads, and uses only the relative polar angles of quads around the center of the lens. The analysis is statistical in nature, and model-free because its conclusions relate to whole classes of models, instead of specific models. The work done here is twofold. Firstly, exploratory analysis is done to check for possible existence of degeneracies. Type I lenses which obey both symmetries mentioned above are found to form a nearly invariant surface in the 3D space of relative image angles. In the same space, lenses that break the double mirror symmetry, grouped as Type II, form two distinct surfaces. In addition, degeneracy in this class of lenses is discovered. A preliminary study of the last group of lenses, Type III, that break both symmetries, is done. Secondly, quad distributions in the 3D space from each of the three families were compared to observed galaxy-lens quads. Three quarters of observed quads were inconsistent with the distribution of quads of Type I lenses. Type II lenses reproduce most individual lens systems but fail to reproduce the population properties of observed quads. Preliminary exploration of Type III lenses shows a very promising agreement with observations. Examples of Type IIIs are lenses with substructure (with clump masses larger than those responsible for flux ratio anomalies in quads), and lenses with luminous or dark nearby perturber galaxies, or line of sight structures.enCosmologyDark matterGalaxiesModel-freeStatisticsSubstructureThesis or Dissertation