Natural braneworlds in six dimensions and the cosmological constant problem

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 search for solutions of the
cosmological constant problem in the realm of extra-dimensional
scenarios. In particular, models with infinite volume extra
dimensions are found to offer a working mechanism, which yet
requires refinement to comply with the observational bounds.