Eggs, Bubbles, and Wormholes in semi-classical quantum gravity

Current observations suggest that our universe is asymptoting towards a de Sitter space with a small amount of vacuum energy. From a quantum field theory perspective, this smallness presents a perplexing puzzle –the cosmological constant problem– and it is the hope that a theory of quantum gravity, such as string theory, provides an opportunity to address it. However, the status of our universe in string theory is not yet clear and it appears fruitful to construct string–inspired models to understand some semi–classical aspects of gravity in a cosmological setting. In chapter 3, we argue that in theories with extra dimensions, such as string theory, the cosmological hierarchy problem can be thought of as the unnaturally large radius of the observable universe in Kaluza–Klein units. An early universe scenario is proposed in which three large spatial dimensions arise through tunneling from a ‘cosmic egg’, an effectively one–dimensional configuration with all spatial dimensions compact and of comparable, small size. A quantum cosmological treatment of a toy model egg predicts that, in a variant of the Hartle–Hawking state, cosmic eggs ‘break’ to form higher–dimensional universes with a small, but positive cosmological constant. Cosmic eggs serve as natural initial conditions for cosmology, whose breaking dynamically relaxes the cosmological constant problem. In chapter 4, motivated by the difficulty in finding explicit de Sitter solutions within string theory, we argue in favor of the recently proposed Dark Bubble model, where a de Sitter cosmology is induced on the surface of a Brown–Teitelboim bubble in a five–dimensional anti–de Sitter space. From a quantum cosmological point of view, the boundary conditions are unambiguously fixed by demanding consistency with the known physics of bubble nucleation; this selects the Vilenkin weighting for the amplitude. In order to generalize the connection between Dark Bubbles and quantum cosmology to include gravitational perturbations, we construct the five–dimensional uplift of the four–dimensional gravitational waves in a de Sitter cosmology. We also use this uplift to explain the interpretation of the apparently negative energy contributions in the effective four–dimensional Einstein equations, which distinguish the Dark Bubble scenario from Randall-Sundrum. In chapter 5, we turn to Euclidean axion wormholes and their status as saddle points in the path integral. We confirm the recent result that Giddings–Strominger wormholes are perturbatively stable saddle points in both the three–form and scalar field formulation of the axion. Our analysis also provides a clean interpretation of the boundary conditions, which seem to have been applied erroneously in the literature.