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Prominent possible explanations for Dark Energy arise from space-times with more than four dimensions, which is motivated by a theoretical unification of gravity with the other fundamental interactions. A geometry with branes moveing in higher-dimensional spacetime may find a natural explanation in the framework of string and M-theory. According to this picture our observed Universe could be a 4-(spacetime)-dimensional domain wall, embedded in extra space dimensions.

Such a scheme offers new, unconventional and promising ways to address cosmological questions. Phenomena that appear strange from the 4-dimensional view might find simple explanations in the higher dimensional theory - in particular questions of the cosmological constant and Dark Energy. An investigation of the cosmological constant within this framework has revealed a so-called self-tuning mechanism where (Dark) energy can flow off a brane into the extra dimensions (bulk), or vice versa. This flow is related to scalar or pseudoscalar fields that are interesting candidates for quintessence.

This project aims to explore the properties of this new form of Dark Energy as well as the phenomenological consequences of these light scalar fields. We first examine the existing static solutions of the dilatonic brane world, which could give information on the equation of state of this form of Dark Energy, expressed as the parameter ω = *p /* ρ . A next step would be the construction of suitable time-dependent solutions to understand the cosmological evolution. This would then also allow new attempts to understand the mechanism of inflation in the early Universe. Due to the complexity of the system a first analysis would consider simple toy models in 5 or 6 dimensions. In a next step one would then try to investigate various realizations of the brane world picture as predicted in the framework of higher dimensional string theories.

A particular point of view for models in six or higher dimensions, with branes of codimension two or higher, describes the branes as singularities in the "bulk geometry". The investigation of the time dependence can then be performed by solving the relevant higher-dimensional field equations in the bulk. In particular, we will investigate the role of dilatation symmetry for the issue of an asymptotically vanishing "cosmological constant".

The change in higher dimensional geometry can appear for an observer in our four-dimensional effetice description as a scalar field - the cosmon (or dilaton). The cosmon wil mediate new macroscopic interactions (cosmodynamics) which may be detectable in the form of an apparent violation of the equivalence principle (differential accelerations between two bodies with equal mass but differing composition) and a cosmological time evolution of the fundamental coupings like the electromagnetic fine structure constant.

The second part of this project aims at the establishment of quantitative relations between the cosmological evolution of Dark Energy, the time variation of fundamental constants and the violation of the equivalence principle. The unknown interaction strength between the cosmon and "ordinary matter" (baryons, electrons, photons) has to be bounded or fixed by current observations like the primordial element abundances from nucleosynthesis, measurements of the variations of the fine structure constant, or tests of the equivalence principle.

The present model aims to bring theoretical concepts of a higher dimensional origin of Dark Energy to the point where observational consequences can be derived. In connection with B1^{?} we will incorporate the observational results on a possible time evolution of Dark Energy from B3-B8^{?}. This will be a vital ingredient for the selection of viable models. As far as a possible coupling between Dark Energy and Dark Matter is concerned we will collaborate with C3. This concerns both the proposal of models as candidates for simulations, and the use of results of C3 for model building.

The more mathematical aspects of the models considered here could profit very much from developments in A3. As part of the models considered here will correspond to so-called warped compactifications, there will be connections to the analysis in A4. The present project provides explicit constructions of solutions in De Sitter space that are closely related to models of the inflationary Universe. This constitutes a link to research in projects A2 and B2^{?}.

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