| This dissertation's main focus is localization of gravity in braneworld models, and the de Sitter/CFT correspondence. We first study a gravitational analog of the Higgs mechanism, by considering localization of gravity in a dilatonic domain wall setup. After giving an elementary model of scalar fluctuations localization on a domain wall, we proceed to study the background and fluctuations of gravity coupled to a scalar field with a potential admitting domain walls. We find that scalar and graviphoton fluctuations in such backgrounds can be completely gauged away, while the graviscalar fluctuations do not have normalizable modes, giving an analogy of the Higgs mechanism for localized gravity. We also study the coupling of brane matter to gravity in this background, and find that for it to be consistent, matter must be conformal.; Motivated by the cosmological constant problem, we then turn our attention to localization of gravity in braneworlds with non-compact extra dimensions. We start with a simple scalar example of fluctuations localization in non-compact extra dimensions. Next we consider gravity localization on a 3-brane in a 6-dimensional bulk, with noncompact (in fact, locally flat) extra dimensions. In such backgrounds we can induce the Einstein-Hilbert term on the brane at the classical level by including higher curvature (Gauss-Bonnet) terms in the bulk. We study (linearized) gravity in the presence of the Einstein-Hilbert term on the brane in this backgrounds and find that, just as in the original Dvali-Gabadadze model with a tensionless brane, gravity is almost completely localized on the brane with ultra-light modes penetrating into the bulk.; With the idea of putting the DGP model into higher codimension we then discuss gravity on non-BPS branes with codimension >2 in an infinite-volume bulk. Such backgrounds are badly singular for delta-function-like branes with non-zero tension, and smoothing out such singularities is non-trivial: for example, using a smooth brane distribution in the extra dimensions results in the presence of an infinite tower of tachyons, while modeling the brave as a spherical shell in the extra dimensions produces inconsistent Einstein equations.; We then turn our attention to fermions in the proposed dS/CFT correspondence. Using the technique of maximally symmetric bitensors, we first calculate the propagator of massive spin 3/2 fields in de Sitter space (massive gravitinos are expected to be present in any embedding of de Sitter space in string theory), and then use our propagator, together with older results for spin 1/2 propagation, to study the dual operators in the conformal field theory. We find that the scaling dimensions of these operators is always complex, rendering the dual conformal field theory nonunitary. This seems to indicate that the correspondence should be reformulated. |
