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Title: Cosmology of braneworld universes
Author: Carvalho, C.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2004
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The motivation of this study is the eventual application to calculating braneworld cosmological perturbations in order to determine observational signatures for the existence of extra dimensions. First, we construct five-dimensional bulk spacetime solutions, empty except for a negative cosmological constant, in the absence of any cosmological perturbations. Taking a higher-dimensional variant of Birkoff’s theorem, we find anti-de Sitter bulk solutions to the five-dimensional Einstein equations exhibiting three-dimensional spatial homogeneity and isotropy. We introduce branes as spacetime trajectories endowed with the same three-dimensional spatial symmetry as the bulk, hence capable of reproducing the observed homogeneity and isotropy of the universe. Second, we analyse the viability of a mechanism for the generation of a braneworld immersed in five-dimensional anti-de Sitter spacetime. An initial phase of de Sitter spacetime, which rapidly tends to an attractor vacuum state, is postulated. Through quantum tunnelling, bubbles of anti-de Sitter nucleate in the background de Sitter spacetime. From the collision of two such bubbles results a four-dimensional surface of constant negative spatial curvature where our four-dimensional universe will be localized. This mechanism has the advantage of explaining the bulk smoothness and horizon problems, of reproducing three-dimensional spatial homogeneity and isotropy, and also of giving rise to a warped geometry with the potential to explain the hierarchy problem. Third, we explore the nature of the brane-bulk interaction with a view towards computing the linearized cosmological perturbations for the models previously constructed. In particular, we focus on the study of the production and propagation of gravitational waves, since these are the only bulk degrees of freedom. We present the study of the quantum field theory of modes of a spring connected to a semi-infinite string in situations of increasing complexity, which exhibit all the qualitative features of the brane-bulk system except for gravitational gauge invariance. The production of gravitons is described by the motion of the spring, with the waves thus produced propagating through the string. A perturbative expansion of the brane propagator in five dimensions is contructed. Fourth, we consider the problem of gravitational gauge fixing for a brane moving on the boundary of the bulk spacetime solutions, its trajectory being determined by the evolution of its stress-energy content. The formulation of boundary conditions is essential for the complete definition of the problem of computing cosmological perturbations on a moving boundary. We derive the boundary conditions for linearized perturbations in a moving brane background spacetime and study the compatibility with the induced Lorentz gauge conditions. Fifth, we work out the effects on the graviton propagator due to the presence of simple forms of matter on the brane, namely a scalar field and a perfect fluid, which reproduce and inflationary and radiation/matter-dominated regimes from the four-dimensional perspective. We derive the boundary conditions modified by the presence of matter on the brane and expand perturbatively the brane and the bulk propagators.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available