Stable, Time-Dependent, Exact Solutions for Brane Models with a Bulk Scalar Field

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflationary, time-dependent solutions of the 3D scale factor on the brane. We also derive the constraints necessary for the stability of these solutions under time-dependent perturbations of the radion field, and we demonstrate the existence of phenomenologically interesting, stable solutions with a positive cosmological constant on the brane.Comment: 24 pages, latex, 4 eps figur

Multigravity in six dimensions: Generating bounces with flat positive tension branes

We present a generalization of the five dimensional multigravity models to six dimensions. The key characteristic of these constructions is that that we obtain solutions which do not have any negative tension branes while at the same time the branes are kept flat. This is due to the fact that in six dimensions the internal space is not trivial and its curvature allows bounce configurations with the above feature. These constructions give for the first time a theoretically and phenomenologically viable realization of multigravity.Comment: 27 pages, 13 figures, typos correcte

Brane World Cosmology with Gauss-Bonnet Interaction

We study a Randall-Sundrum model modified by a Gauss-Bonnet interaction term. We consider, in particular, a Friedmann-Robertson-Walker metric on the brane and analyse the resulting cosmological scenario. It is shown that the usual Friedmann equations are recovered on the brane. The equation of state relating the enery density and the pressure is uniquely determined by the matching conditions. A cosmological solution with negative pressure is found.Comment: 9 pages, revtex styl

Scalar brane backgrounds in higher order curvature gravity

We investigate maximally symmetric brane world solutions with a scalar field. Five-dimensional bulk gravity is described by a general lagrangian which yields field equations containing no higher than second order derivatives. This includes the Gauss-Bonnet combination for the graviton. Stability and gravitational properties of such solutions are considered, and we particularily emphasise the modifications induced by the higher order terms. In particular it is shown that higher curvature corrections to Einstein theory can give rise to instabilities in brane world solutions. A method for analytically obtaining the general solution for such actions is outlined. Genericaly, the requirement of a finite volume element together with the absence of a naked singularity in the bulk imposes fine-tuning of the brane tension. A model with a moduli scalar field is analysed in detail and we address questions of instability and non-singular self-tuning solutions. In particular, we discuss a case with a normalisable zero mode but infinite volume element.Comment: published versio

A Novel Mass Hierarchy and Discrete Excitation Spectra from Quantum-Fluctuating D-branes

We elaborate further on a recently proposed scenario for generating a mass hierarchy through quantum fluctuations of a single D3 brane, which represents our world embedded in a bulk five-dimensional space time. In this scenario, the quantum fluctuations of the D3-brane world in the bulk direction, quantified to leading order via a `recoil' world-sheet logarithmic conformal field theory approach, result in the dynamical appearance of a supersymmetry breaking (obstruction) scale alpha. This may be naturally taken to be at the TeV range, in order to provide a solution to the conventional gauge-hierarchy problem. The bulk spatial direction is characterized by the dynamical appearance of an horizon located at +- 1/alpha, inside which the positive energy conditions for the existence of stable matter are satisfied. To ensure the correct value of the four-dimensional Planck mass, the bulk string scale M_s is naturally found to lie at an intermediate energy scale of 10^{14} GeV. As an exclusive feature of the D3-brane quantum fluctuations (`recoil') we find that, for any given M_5, there is a discrete mass spectrum for four-dimensional Kaluza-Klein (KK) modes of bulk graviton and/or scalar fields. KK modes with masses 0 <= m < sqrt{2}alpha << M_s are found to have wavefunctions peaked, and hence localized, on the D3 brane at z=0.Comment: 21 pages latex, three eps figures incorporate

The Dynamics of Brane-World Cosmological Models

Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or {\em brane} embedded in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall-Sundrum-type models are self-consistent and simple and allow for an investigation of the essential non-linear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology.Comment: Einstein Centennial Review Article: to appear in CJ