Natural braneworlds in six dimensions and the cosmological constant problem Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 05/05

The observed accelerated expansion of the universe is successfully parameterized by a cosmological constant. However, since this parameter in Einstein's equations is not protected against quantum corrections, the observed and theoretically expected value vastly differ, thus giving rise to the cosmological constant problem. In this thesis, the issue is addressed by embedding our universe--represented by a brane--in a six-dimensional bulk spacetime, where the cosmological constant plays the role of a brane tension, which then no longer needs to imply an expansion of the three apparent spatial dimensions; rather, it curves the extra space and hence stays hidden from a brane observer. In this context, the crucial question is whether this so-called degravitation mechanism may be implemented in a phenomenologically viable and 't Hooft natural way. Corresponding answers will be given in the case of four different models.
The main part of this thesis has its focus on the 6D brane induced gravity model--a higher-dimensional generalization of the Dvali-Gabadadze-Porrati model--according to which a brane with sub-critical tension curves the bulk into a cone of infinite spatial extent.
First, it is shown that the model is free of ghost instabilities only if the tension is not unnaturally small.
This in turn opens a window of opportunity to study theoretically consistent modified cosmologies. In this context, it is shown that a homogeneous and isotropic brane acts as an antenna that emits and absorbs cylindrically symmetric Einstein-Rosen waves.
We encounter two interesting types of solutions--sub-critical ones, which feature dynamical degravitation but are incompatible with observations, as well as compact super-critical ones, which still might be phenomenologically viable but certainly not technically natural. While this clearly shows that the cosmological constant problem cannot be solved in a 6D version of the model, our results point towards higher-dimensional constructions as the remaining playground for future research.
Next, we introduce a new two-brane model where a thick super-critical brane curves the extra space into a cigar that closes in a microscopically thin sub-critical brane, representing our universe. In the case both branes only host a tension, we derive fully analytic solutions, which correspond to a de Sitter phase on our brane and are hence phenomenologically promising. Unfortunately, as a fine-tuning of the brane tension is required, they are not technically natural. The failure is attributed to the compactness of the extra space.
To further exemplify the virtue of infinite volume extra dimensions, we devise a hybrid model where the brane is wrapped around an infinitely long cylinder of microscopic width. This construction turns out to be the minimal setup that features bulk waves as a dynamical ingredient of a modified cosmology. We find that, due to the existence of an infinitely large dimension, the system admits a degravitating solution. While being conceptually interesting, a supernova fit shows that the corresponding 4D cosmology cannot describe our universe.
Finally, we turn to the model of supersymmetric large extra dimensions that had been claimed to successfully address the cosmological constant problem. Here, a Maxwell flux stabilizes the extra space that has the shape of a rugby ball.
We critically review the corresponding mechanism, and find that a vanishing brane curvature--as required by the degravitation idea--is only ensured by a scale invariant brane sector, which however leads to an unavoidable parameter constraint due to a flux quantization condition.
In a second step, we generalize our analysis to solutions that admit a de Sitter phase on the brane. Provided the model parameters are not tuned, we find that either the brane curvature or the volume of the extra space exceeds its phenomenological bound by many orders of magnitude.
Our results significantly narrow down the s