Dynamical Stability of Six-dimensional Warped Flux Compactification

We show the dynamical stability of a six-dimensional braneworld solution with warped flux compactification recently found by the authors. We consider linear perturbations around this background spacetime, assuming the axisymmetry in the extra dimensions. The perturbations are expanded by scalar-, vector- and tensor-type harmonics of the four-dimensional Minkoswki spacetime and we analyze each type separately. It is found that there is no unstable mode in each sector and that there are zero modes only in the tensor sector, corresponding to the four-dimensional gravitons. We also obtain the first few Kaluza-Klein modes in each sector.Comment: 46 pages, 8 figures. Version to appear in JCA

Brane cosmological solutions in six-dimensional warped flux compactifications

We study cosmology on a conical brane in the six-dimensional Einstein-Maxwell-dilaton system, where the extra dimensions are compactified by a magnetic flux. We systematically construct exact cosmological solutions using the fact that the system is equivalently described by (6+n)-dimensional pure Einstein-Maxwell theory via dimensional reduction. In particular, we find a power-law inflationary solution for a general dilatonic coupling. When the dilatonic coupling is given by that of Nishino-Sezgin chiral supergravity, this reduces to the known solution which is not inflating. The power-law solution is shown to be the late-time attractor. We also investigate cosmological tensor perturbations in this model using the (6+n)-dimensional description. We obtain the separable equation of motion and find that there always exist a zero mode, while tachyonic modes are absent in the spectrum. The mass spectrum of Kaluza-Klein modes is obtained numerically.Comment: 12 pages, 2 figures; v2: references added; v3: version published in JCA

Hybrid compactifications and brane gravity in six dimensions

We consider a six-dimensional axisymmetric Einstein-Maxwell model of warped braneworlds. The bulk is bounded by two branes, one of which is a conical 3-brane and the other is a 4-brane wrapped around the axis of symmetry. The latter brane is assumed to be our universe. If the tension of the 3-brane is fine-tuned, it folds the internal two-dimensional space in a narrow cone, making sufficiently small the Kaluza-Klein circle of the 4-brane. An arbitrary energy-momentum tensor can be accommodated on this ring-like 4-brane. We study linear perturbations sourced by matter on the brane, and show that weak gravity is apparently described by a four-dimensional scalar-tensor theory. The extra scalar degree of freedom can be interpreted as the fluctuation of the internal space volume (or that of the circumference of the ring), the effect of which turns out to be suppressed at long distances. Consequently, four-dimensional Einstein gravity is reproduced on the brane. We point out that as in the Randall-Sundrum model, the brane bending mode is crucial for recovering the four-dimensional tensor structure in this setup.Comment: 15 pages, 2 figures; v2: references added; v3: accepted for publication in Class. Quant. Gra

Instability of brane cosmological solutions with flux compactifications

We discuss the stability of the higher-dimensional de Sitter (dS) brane solutions with two-dimensional internal space in the Einstein-Maxwel theory. We show that an instability appears in the scalar-type perturbations with respect to the dS spacetime. We derive a differential relation which has the very similar structure to the ordinary laws of thermodynamics as an extension of the work for the six-dimensional model [20]. In this relation, the area of dS horizon (integrated over the two internal dimensions) exactly behaves as the thermodynamical entropy. The dynamically unstable solutions are in the thermodynamically unstable branch. An unstable dS compactification either evolves toward a stable configuration or two-dimensional internal space is decompactified. These dS brane solutions are equivalent to the accelerating cosmological solutions in the six-dimensional Einstein-Maxwell-dilaton theory via dimensional reduction. Thus, if the seed higher-dimensional solution is unstable, the corresponding six-dimensional solution is also unstable. From the effective four-dimensional point of view, a cosmological evolution from an unstable cosmological solution in higher dimensions may be seen as a process of the transition from the initial cosmological inflation to the current dark energy dominated Universe.Comment: 11 pages, 3 figures, references added, to appear in CQ