In this thesis I will be examining the study of the large scale structure of the universe. In particular, I will be looking at the role of peculiar motions of galaxies - ie motions that deviate from the uniform Hubble expansion of the universe. The study of these motions holds much promise for cosmology, but there are considerable problems with measuring and mapping them, a number of which I will be addressing in the course of this work. However, I will start in chapter 1 by giving a brief introduction to the theory behind the formation of structure in the universe and the current state of our knowledge about its form and history. The framework provided by the Big Bang theory of the origins of the universe, has withstood a number of observational tests with remarkable success and this has enabled cosmologists to extend and refine the theory. This enlarged model can also be tested by observations and in its success or failure, improve our understanding and narrow the limits of future research. In chapter 2, therefore, I will describe one of the most powerful set of observational tools - the measurement of the local velocity and density fields. Inherent in the Big Bang theory, and almost any other reasonable explanation of the universe, is the idea of formation and evolution of structure. The velocity and density fields tell us about the current state of that evolution and, therefore, will set very strong constraints on any theory. However, as I will show, the measurement and analysis of such fields is a complicated and difficult business. In particular, many methods rely on estimation of the distances to galaxies and this estimation is subject to very large errors. In the latter half of the chapter, I will be considering this problem and looking at some of the most popular distance estimators and some of the systematic errors or biases that they can introduce to field recoveries. The most commonly used estimators (Tully-Fisher and Dn-sigma techniques) rely on a strong correlation between two observable properties of each galaxy - one that varies with distance and another that is distance-independent. Therefore, by using the distance-independent quantity to estimate the absolute values of the dependent observable, the distance can be estimated. However, one of the major problems with such distance estimation techniques is calibration - exactly how are the two parameters of the chosen relation correlated? In chapter 3 I will describe a new method of calibration that attempts to combine a number of clusters of galaxies together into one large cluster that can then be used as a calibration yardstick. This is an extension of the standard technique where a single cluster is used. While describing this technique, I will also demonstrate its efficacy with several carefully devised tests that will show clearly how it improves over the single-cluster approach. Given a set of distance estimates, we now wish to derive some information about the local velocity field. One very successful method for doing this is described in chapter 4 - the POTENT method (Bertschinger and Dekel, 1989). With this technique, expansion of the universe is removed from the velocity field by comparing the recession velocities of galaxies with their estimated distances and the resultant smoothed peculiar velocity field recovered under the assumption of potential flow. I will describe my implementation of the method and go on to test it with a variety of different forms of distance estimator thereby demonstrating the large biases that can result (especially the so-called Malmquist bias). Although a number of "corrections" for this bias already exist, I will show that none are ideal and when applied in the wrong situation or without a full understanding of the properties of the chosen distance estimator, the results can be far worse than with no correction at all. Chapter 5, therefore, is concerned with a number of techniques I have developed during the course of this thesis to improve on this situation. The first of these attempts to minimise the problems by performing as much of the analysis as possible in redshift-space, thereby avoiding much of the use of distance estimates. However, although successful for simple tests, this proves to be inadequate when confronted with a realistically complicated situation. More successful is an iterative technique based around Monte Carlo error estimates that gradually adjusts an estimate of the velocity field until its recovery (with biases) matches the recovery with the actual data. This method has the particular advantage of making no assumptions about the causes of the various biases, but simply tries to estimate their effect and remove them. The results are noticeably better than any other method in all the tests performed. Finally in this chapter, an attack is made upon the random errors in POTENT recoveries.(Abstract shortened by ProQuest.).
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