The diffeomorphism field is introduced to the physics literature in [1] where it arises as a background field coupled to Polyakov’s quantum gravity in two dimensions, where Einstein’s gravity is trivial. Moreover, it is seen in many ways as the gravitational analog of the Yang-Mills field. This raises the question of whether the diffeomorphism field exists in higher dimensions, playing an essential role in gravity either by supplementing Einstein’s theory or by modifying it. With this motivation, several distinct theories governing the dynamics of the diffeomorphism field have been constructed and developed by mimicking the construction of the Yang-Mills theory from the Kac-Moody algebra. This analogy, however, is not perfect and there are many subtleties and difficulties encountered. This thesis constitutes a further development. The previously proposed theories are carefully examined; certain subtleties and problems in them have been discovered and made apparent. Some of these problems have been solved, and for others possible routes to follow have been laid down. Finally, other geometric approaches than the ones followed before are investigated.

The discovery of cosmic acceleration has prompted the need for a new understanding of cosmology. The presence of this acceleration is often described as the dark energy problem or the Lambda problem.The simplest explanation is that the acceleration is due to addition of a cosmological constant to Einstein's equation, but this resolution is unsatisfactory as it leaves several unanswered questions. Although General Relativity has been tested in the strong-field limit, the apparent dark energy may be urging us to consider experimental cosmology as such a test for large scales. In this vein, I have pursued a study of modifications to Einstein's gravity as well as possible related quantum gravity phenomenology. Not only must the details of modified gravities be worked out, but their impact on other astrophysics must be checked. For example, structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified gravity implement the Press & Schechter formalism. I explore the potential for universality in the Press & Schechter formalism and what dark matter haloes may be able to tell us about cosmology.

The discovery of cosmic acceleration has prompted the need for a new understanding of cosmology. The presence of this acceleration is often described as the dark energy problem or the Lambda problem.The simplest explanation is that the acceleration is due to addition of a cosmological constant to Einstein's equation, but this resolution is unsatisfactory as it leaves several unanswered questions. Although General Relativity has been tested in the strong-field limit, the apparent dark energy may be urging us to consider experimental cosmology as such a test for large scales. In this vein, I have pursued a study of modifications to Einstein's gravity as well as possible related quantum gravity phenomenology. Not only must the details of modified gravities be worked out, but their impact on other astrophysics must be checked. For example, structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified gravity implement the Press & Schechter formalism. I explore the potential for universality in the Press & Schechter formalism and what dark matter haloes may be able to tell us about cosmology.

The discovery of cosmic acceleration has prompted the need for a new understanding of cosmology. The presence of this acceleration is often described as the dark energy problem or the Lambda problem.The simplest explanation is that the acceleration is due to addition of a cosmological constant to Einstein's equation, but this resolution is unsatisfactory as it leaves several unanswered questions. Although General Relativity has been tested in the strong-field limit, the apparent dark energy may be urging us to consider experimental cosmology as such a test for large scales. In this vein, I have pursued a study of modifications to Einstein's gravity as well as possible related quantum gravity phenomenology. Not only must the details of modified gravities be worked out, but their impact on other astrophysics must be checked. For example, structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified gravity implement the Press & Schechter formalism. I explore the potential for universality in the Press & Schechter formalism and what dark matter haloes may be able to tell us about cosmology.

The discovery of cosmic acceleration has prompted the need for a new understanding of cosmology. The presence of this acceleration is often described as the dark energy problem or the Lambda problem.The simplest explanation is that the acceleration is due to addition of a cosmological constant to Einstein's equation, but this resolution is unsatisfactory as it leaves several unanswered questions. Although General Relativity has been tested in the strong-field limit, the apparent dark energy may be urging us to consider experimental cosmology as such a test for large scales. In this vein, I have pursued a study of modifications to Einstein's gravity as well as possible related quantum gravity phenomenology. Not only must the details of modified gravities be worked out, but their impact on other astrophysics must be checked. For example, structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified gravity implement the Press & Schechter formalism. I explore the potential for universality in the Press & Schechter formalism and what dark matter haloes may be able to tell us about cosmology.

Thesis (Ph.D.)--Tufts University, 2002. / Adviser: L. H. Ford. Submitted to the Dept. of Physics. Includes bibliographical references (leaves 161-165). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, June 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 118-135). Also available via the World Wide Web.

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This thesis is a study of classical and quantum gravity with Ashtekar variables. The Ashtekar constraints are shown to capture the essence of the constraints and constraint algebra of General Relativity in four dimensions. A classification scheme of the solution space of the Ashtekar constraints is proposed and the corresponding physics is investigated. The manifestly covariant equations of motion for the Ashtekar variables are derived. Explicit examples are discussed and new classical solutions of General Relativity are constructed by exploiting the properties of the Ashtekar variables. Non-perturbative canonical quantization of the theory is performed. The ordering of the quantum constraints as well as the formal closure of the quantum constraint algebra are explored. A detailed Becchi-Rouet-Stora-Tyutin (BRST) analysis of the theory is given. The results demonstrate explicitly that in quantum gravity, fluctuations in topology can occur and there are strong evidences of phases in the theory. There is a phase which is described by a topological quantum field theory (TQFT) of the Donaldson-Witten type and an Abelian antiinstanton phase wherein self-interactions of the gravitational fields produce symmetry breaking from SO(3) to U(1). The full theory is much richer and includes fluctuations which bring the system out of the various restricted sectors while preserving diffeomorphism invariance. Invariants of the quantum theory with are constructed through BRST descents. They provide a clear and systematic characterization of non-local observables in quantum gravity, and can yield further differential invariants of four-manifolds. / Ph. D.