AbstractsAstronomy & Space Science

Modified gravity and cosmology with two extra dimensions

by Robert Schneider




Institution: Ludwig-Maximilians-Universität
Department:
Year: 2016
Posted: 02/05/2017
Record ID: 2064997
Full text PDF: https://edoc.ub.uni-muenchen.de/19372/


Abstract

In this thesis, we investigate the gravitational consequences of theories in which the four spacetime dimensions of our universe are augmented by two spatial extra dimensions. More specifically, the focus is on braneworld scenarios, where our world is confined on a hypersurface in the higher-dimensional bulk, allowing the extra dimensions to be large or even infinite. Our main motivation for studying such models is that they could in principle be able to solve the cosmological constant (CC) problem via degravitation: the CC only curves the extra space, leaving the brane geometry flat. A major difference to the simpler case of a codimension-one brane is that here, gravitational waves can be emitted into the bulk, even at the 3D homogeneous and isotropic level, as is relevant for cosmology. Therefore, we first analyze the question how an outgoing wave boundary condition can be implemented, which is necessary in order to obtain a closed set of modified Friedmann equations predicting the cosmological on-brane evolution. We find that a potential tool from the literature, provided by a certain decomposition of the Weyl tensor - while being applicable to plane gravitational waves - fails for cylindrical waves. This failure is related to the fact that it is already impossible to locally separate incoming from outgoing linear cylindrical waves (on flat spacetime), as we demonstrate by explicitly deriving the corresponding nonreflecting boundary condition, which is nonlocal in time. We then consider a generalization of the Dvali-Gabadadze-Porrati (DGP) model, containing an additional compact on-brane dimension on top of the one infinite codimension. Since here the 3D maximally symmetric brane emits plane waves, the Weyl tensor criterion can be used to exclude incoming bulk waves, and we derive the resulting Friedmann equations. If the compact dimension is stabilized, DGP cosmology is recovered, but we find indications that the stabilization should break down when the CC starts to dominate, which would lead to additional, potentially interesting late time modifications. If, on the other hand, the compact direction is allowed to expand freely, there are dynamically degravitating solutions - which, however, lack a 4D regime and are thus ruled out, as we demonstrate by fitting to supernova data. Next, we turn to the codimension-two version of the DGP model. By numerically solving the full nonlinear coupled bulk-brane system for cosmological symmetries on the (regularized) brane, we show that in some region of parameter space, a CC - but also any other fluid component - gets degravitated dynamically, and a static geometry is approached via the emission of Einstein-Rosen waves. For other model parameters, pathological super-accelerating solutions are encountered. The origin of this unstable behavior is traced back to a tachyonic ghost mode which is identified in this parameter region by studying linear metric perturbations around a nontrivial pure tension background. While confirming the ghost result on Minkowski from the… Advisors/Committee Members: Hofmann, Stefan (advisor).