Scaling Solutions to 6D Gauged Chiral Supergravity

We construct explicitly time-dependent exact solutions to the field equations of 6D gauged chiral supergravity, compactified to 4D in the presence of up to two 3-branes situated within the extra dimensions. The solutions we find are scaling solutions, and are plausibly attractors which represent the late-time evolution of a broad class of initial conditions. By matching their near-brane boundary conditions to physical brane properties we argue that these solutions (together with the known maximally-symmetric solutions and a new class of non-Lorentz-invariant static solutions, which we also present here) describe the bulk geometry between a pair of 3-branes with non-trivial on-brane equations of state.Comment: Contribution to the New Journal of Physics focus issue on Dark Energy; 28 page

Kicking the Rugby Ball: Perturbations of 6D Gauged Chiral Supergravity

We analyze the axially-symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the nonconical for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam-Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equations, and all other modes have positive squared mass. In the special case of the conical solutions, including (but not restricted to) the unwarped `rugby-ball' solutions, we find closed-form expressions for the mode functions in terms of Legendre and Hypergeometric functions. In so doing we show how to match the asymptotic near-brane form for the solution to the physics of the source branes, and thereby how to physically interpret perturbations which can be singular at the brane positions.Comment: 21 pages + appendices, references adde

Codimension Two Branes and Distributional Curvature

In general relativity, there is a well-developed formalism for working with the approximation that a gravitational source is concentrated on a shell, or codimension one surface. By contrast, there are obstacles to concentrating sources on surfaces that have a higher codimension, for example, a string in a spacetime with dimension greater than or equal to four. Here it is shown that, by giving up some of the generality of the codimension one case, curvature can be concentrated on submanifolds that have codimension two. A class of metrics is identified such that (1) the scalar curvature and Ricci densities exist as distributions with support on a co-dimension two submanifold, and (2) using the Einstein equation, the distributional curvature corresponds to a concentrated stress-energy with equation of state p equals minus the energy density, where p is the isotropic pressure tangent to the submanifold. This is the appropriate stress-energy to describe a self-gravitating brane that is governed by an area action, or a brane world deSitter cosmology. The possibility of having a different equation of state arise from a wider class of metrics is discussed.Comment: 18 pages; v2 references added; typos corrected, references added; additional references adde

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

Low energy effective theory on a regularized brane in 6D gauged chiral supergravity

We derive the low energy effective theory on a brane in six-dimensional chiral supergravity. The conical 3-brane singularities are resolved by introducing cylindrical codimension one 4-branes whose interiors are capped by a regular spacetime. The effective theory is described by the Brans-Dicke (BD) theory with the BD parameter given by $\omega_{\rm BD}=1/2$. The BD field is originated from a modulus which is associated with the scaling symmetry of the system. If the dilaton potentials on the branes preserve the scaling symmetry, the scalar field has an exponential potential in the Einstein frame. We show that the time dependent solutions driven by the modulus in the four-dimensional effective theory can be lifted up to the six-dimensional exact solutions found in the literature. Based on the effective theory, we discuss a possible way to stabilize the modulus to recover standard cosmology and also study the implication for the cosmological constant problem.Comment: 12 pages, 1 figur

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

Lectures on Cosmic Inflation and its Potential Stringy Realizations

These notes present a brief introduction to Hot Big Bang cosmology and Cosmic Inflation, together with a selection of some recent attempts to embed inflation into string theory. They provide a partial description of lectures presented in courses at Dubrovnik in August 2006, at CERN in January 2007 and at Cargese in August 2007. They are aimed at graduate students with a working knowledge of quantum field theory, but who are unfamiliar with the details of cosmology or of string theory.Comment: 68 pages, lectures given at Dubrovnik, Aug 2006; CERN, January 2007; and Cargese, Aug 200

Technical Naturalness on a Codimension-2 Brane

We compute how threshold effects obtained by integrating out a heavy particle localized on a codimension-2 brane influence the properties of the brane and the bulk fields it sources in D=d+2 dimensions. We do so using a recently developed formalism for matching the characteristics of higher codimension branes to the properties of the bulk fields they source. We show that although the dominant dependence on a heavy mass M that is induced in the low-energy codimension-2 tension has the generic size expected, T_2 \propto M^d, the very-low-energy effective potential governing the on-brane curvature once bulk KK modes are integrated out can be additionally suppressed, by factors of order k^2 M^d, where k is the bulk gravitational coupling. In the special case of a codimension-2 brane in a 6D supersymmetric bulk we also estimate the size of the contributions of short-wavelength bulk loops near the brane, and find these can be similarly suppressed