Die Methode der nichtlokalen effektiven Wirkung in höherdimensionalen Raumzeitmodellen

Among the most promising candidates for a unified description of quantum <br>theory and gravitation is superstring theory. It predicts the existence of <br>multidimensional stable objects called "branes" (short for membranes). On <br>these branes open strings can end, which also means that the gauge fields <br>associated with the ends of a string reside on the branes. Gauge fields, <br>rather than spreading through the entire ten-dimensional spacetime of <br>superstring theory, are thus confined to these lower-dimensional objects. This <br>led to the proposal that the universe we inhabit could be a three-dimensional <br>brane on which all matter consisting of gauge fields is trapped. In string <br>theory, gravity is mediated by the exchange of closed strings and therefore is <br>not restricted to the branes but propagates through the whole <br>higher-dimensional spacetime, commonly called bulk. The shape of the bulk can <br>be constrained because no deviations from four-dimensional gravity have yet <br>been observed. <br> <br>The study concentrates on a specific type of such "braneworld" models, the <br>Randall-Sundrum two-brane model. In this model the bulk is a slice of five <br>dimensional anti-de Sitter space having an orbifold at the position of both <br>branes. The brane tensions have the same magnitude but opposite signs and are <br>fine-tuned to the bulk cosmological constant in such a way that a flat metric <br>is induced on the branes. For this model the nonlocal braneworld action is <br>constructed in a holographic setup alternative to Kaluza-Klein description: <br>the action is written as a functional of the two metric and radion fields on <br>the branes. This action effectively describes the dynamics of the <br>gravitational field both on branes and in the bulk in terms of brane <br>geometries directly accessible for observations. The nonlocal form factors of <br>the action incorporate a cumulative effect of the bulk Kaluza-Klein <br>modes. Also the reduced version of this action is considered which is obtained <br>by integrating out the fields on the negative-tension brane invisible from the <br>viewpoint of an observer on the positive tension brane, "our universe". This <br>effective action features a nontrivial transition (anti-de Sitter flow) <br>between the local and nonlocal phases of the theory associated with the limits <br>of small and large brane separation. The results confirm a braneworld scenario <br>with diverging (repulsive) branes and suggest possible new implications of <br>this phase transition in brane cosmology. The relation of the nonlocal method <br>to the holographic description of braneworlds with an anti-de Sitter bulk by <br>means of the Graham-Feffermann coordinate system is examined. <br> <br>Using the Randall-Sundrum model as an example a phenomenologically important <br>generic aspect of braneworld models is revealed. Braneworld models with <br>non-factorizable geometries can feature extremely light massive gravitons. If <br>astrophysical objects have quadrupole moments oscillating at high frequencies <br>they might therefore produce gravitational waves which are a superposition of <br>the massless and one or more massive modes. As the massive components have <br>propagation speeds below the speed of light, the superposition of the modes <br>will show an interference pattern. This interference will manifest itself as <br>oscillations in the intensity of a gravitational wave. The oscillation length <br>depends on the brane distance parameterized by the non-linear radion <br>field. This led to the name radion-induced graviton oscillations for the <br>predicted effect. In the Randall-Sundrum model in particular waves from the <br>negative tension brane exhibit strong oscillations on the positive tension <br>brane. Although these waves seem strongly suppressed at first sight by the <br>geometry of the bulk M-theory scaling arguments suggest that oscillations of <br>gravitational waves from the negative-tension brane may actually become a <br>relevant effect for gravitational wave astronomy. Other simple braneworld <br>models are discussed which show a strong mixing of modes and large amplitude <br>modulations although connected with oscillation lengths of cosmological <br>scales, which remain therefore unobservable. Graviton oscillations are treated <br>both in a derivative expansion of the effective action and in an expansion of <br>the effective four-dimensional Green function.

Author dc:creator

• Rathke, Andreas

Contributors dc:contributor

• Römer, Hartmann

• cosmology
• effective action
• brane
• extra dimensions
• gravitational wave

Repository record source_url

https://freidok.uni-freiburg.de/data/1159

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:1159