Fischler, Willy1558558722008-08-282008-08-282006http://hdl.handle.net/2152/2744textThe observation that we are living in a Universe that is expanding at an ever-increasing rate is a major challenge for any fundamental theory. The most obvious explanation for an accelerating Universe is a positive cosmological constant, but we do not really know how to do quantum field theory or string theory in spacetimes that are not asymptotically flat. In this thesis, we address various issues that arise in this general context. The problems we address include the stability and evolution of de Sitter-like compactifications, the possibility of defining a quantum theory in de Sitter space using quantum groups, and finally, the classical evolution of thin shells (boundaries of new phase bubbles) in an inhomogeneous Universe with positive Λ.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.CosmologyQuantum gravityThesis