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THE ACTION VARIATIONAL PRINCIPLE
IN COSMOLOGY

Trond Hjorteland
Institute of Theoretical Astrophysics
University of Oslo

figure42

Thesis submitted for the degree of Candidatus Scientiarum
at the University of Oslo
Oslo, June 1999





We are all in the gutter,
but some of us are looking at the stars.

- Oscar Wilde





THE ACTION VARIATIONAL PRINCIPLE
IN COSMOLOGY

Trond Hjorteland
Institute of Theoretical Astrophysics
University of Oslo

Abstract

During the last decade, the action variational principle of Peebles has proven to be a very applicable tool in the study of the formation of large-scale structures in the immediate neighbourhood of the Milky Way. It provides us with the mean to recreate the orbits of the galaxies from epochs early in the history of the Universe until the present, which in turn opens for a closer study of a number of subjects concerning the evolution of the Universe. This study will give a thorough presentation of this variational principle and its areas of application, with an emphasis on the numerical aspect. In practise, the use of the action variational principle is a question of numerical optimization, a side of the method which previously has not been considered in detail. The major part of this study is therefore devoted to the testing of several different optimizing methods, attempting to locate the most efficient one. Trials have indicated that the performance of the methods varies considerably with certain properties of the system of mass tracers; e.g. size. The general consensus from numerical literature is that optimizing methods using the second-derivative of the action works best for small systems, while for large systems, the methods using only the first-derivative are preferable. The results here indicate that a combination of these two types of methods work best when having the parameterization of the orbits. In addition to these tests, the action variational principle has also been applied to a system consisting of 22 mass tracers in the Local Group and its immediate neighbourhood, where a couple of newly discovered galaxies has been included. The distances to some of the more distant mass tracers have been adjusted to give a better fit between predicted and observed radial velocities.

Thesis submitted for the degree of Candidatus Scientiarum
at the University of Oslo
Oslo, June 1999





To Natalie





Acknowledgment

There are quite a few people that have been very important in the development of this thesis, and to whom I am eternally grateful: Mikel P. Susperregi for answering all my questions patiently and professionally during the horrid initiating part of the study; Sverre Aarseth for providing me with the NBODY1 code, and for helping me implementing it; P. J. E. Peebles for constructive criticism and suggestions, and for developing the method in the first place; Per B. Lilje for being my supervisor; Mauro Giavalisco, Raymond Laflamme, Stein Vidar Haugan, and Frode Hansen for taking so much out of their precious time to answer my questions and making sure that I kept in touch with cosmology through fascinating discussions; Andreas Botnen, Viggo Hansteen, Olav Dahl, Mats Carlsson, and Torben Leifsen for all their help and assistance with numerical analysis and programming.

There are also quite a few people who have helped and assisted me in a non-professional way, making sure that I kept in touch with the social aspect of life: Terje, Frank, Ellen, Ingunn, Caroline, Vidar, Are-Morten, Andreas, Margrethe, and rest of the students and ``inmates'' at ITA; Gotham Nights and all the people connected with it, especially the members of the committee; all the people that I have been fortunate enough to live with during my time as a student, especially Janina; friends and family that I left behind in my quest for the Universe. At last, a special thanks to Natalie for all her love and support--this thesis is dedicated to you.

Blindern, 25th of June, 1999
Trond Hjorteland




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Trond Hjorteland
Mon Jul 5 02:59:28 MET DST 1999