Asymptotic behaviour of a class of inhomogeneous scalar field cosmologies

The asymptotic behaviour of a class of inhomogeneous scalar field cosmologies with a Liouville type of potential is studied. We define a set of new variables for which the phase space of the system of Einstein equations is bounded. This allows us to perform a complete analysis of the evolution of these cosmologies. We also discuss the extension of the cosmic no-hair theorem.Comment: 23 pages, latex, 3 figures, to appear in J. Math. Phys., figures also available tarred and gzip'ed at http://tp.lc.ehu.es/figures.g

Schwarzschild Black Branes and Strings in higher-dimensional Brane Worlds

We consider branes embedded in spacetimes of codimension 1 and 2, with a warped metric tensor for the subspace parallel to the brane. We study a variety of brane-world solutions arising by introducing a Schwarzschild-like black hole metric on the brane and we investigate the properties of the corresponding higher-dimensional spacetime. We demonstrate that normalizable bulk modes lead to a vanishing flow of energy through the naked singularities. From this point of view, these singularities are harmless. (28 refs)

Gravitating global defects: the gravitational field and compactification

We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater or equal 3. We will see that the general effect of a global defect is to introduce a deficit solid angle. We also show how the same kind of scalar field configurations can be used for spontaneous compactification of "n" extra dimensions on an n-sphere.Comment: Uses revte

Inflating magnetically charged braneworlds

Numerical solutions of Einstein, scalar, and gauge field equations are found for static and inflating defects in a higher-dimensional spacetime. The defects have $(3+1)$-dimensional core and magnetic monopole configuration in $n=3$ extra dimensions. For symmetry-breaking scale $\eta$ below the critical value $\eta_c$, the defects are characterized by a flat worldsheet geometry and asymptotically flat extra dimensions. The critical scale $\eta_c$ is comparable to the higher-dimensional Planck scale and has some dependence on the gauge and scalar couplings. For $\eta=\eta_c$, the extra dimensions degenerate into a `cigar', and for $\eta>\eta_c$ all static solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. The inflating solutions have de Sitter worldsheets and cigar geometry in the extra dimensions. Exact analytic solutions describing the asymptotic behavior of these inflating monopoles are found and the parameter space of these solutions is analyzed.Comment: 35 pages, revtex, 18 eps figure

Stability of inflating branes in a texture

We investigate the stability of inflating branes embedded in an O(2) texture formed in one extra dimension. The model contains two 3-branes of nonzero tension, and the extra dimension is compact. When the gravitational perturbation is applied, the vacuum energy which is responsible for inflation on the branes stabilizes the branes if the symmetry-breaking scale of the texture is smaller than some critical value. This critical value is determined by the particle-hierarchy scale between the two branes, and is smaller than the 5D Planck-mass scale. The scale of the vacuum energy can be considerably low in providing the stability. This stability story is very different from the flat-brane case which always suffers from the instability due to the gravitational perturbation.Comment: 16 pages, 5 eps figures, revte

On the evolution of a large class of inhomogeneous scalar field cosmologies

The asymptotic behaviour of a family of inhomogeneous scalar field cosmologies with exponential potential is studied. By introducing new variables we can perform an almost complete analysis of the evolution of these cosmologies. Unlike the homogeneous case (Bianchi type solutions), when k^2<2 the models do not isotropize due to the presence of the inhomogeneitiesComment: 23 pages, 1 figure. Submitted to Classical and Quantum Gravit

Locally Localized Gravity Models in Higher Dimensions

We explore the possibility of generalizing the locally localized gravity model in five space-time dimensions to arbitrary higher dimensions. In a space-time with negative cosmological constant, there are essentially two kinds of higher-dimensional cousins which not only take an analytic form but also are free from the naked curvature singularity in a whole bulk space-time. One cousin is a trivial extension of five-dimensional model, while the other one is in essence in higher dimensions. One interesting observation is that in the latter model, only anti-de Sitter ($AdS_p$) brane is physically meaningful whereas de Sitter ($dS_p$) and Minkowski ($M_p$) branes are dismissed. Moreover, for $AdS_p$ brane in the latter model, we study the property of localization of various bulk fields on a single brane. In particular, it is shown that the presence of the brane cosmological constant enables bulk gauge field and massless fermions to confine to the brane only by a gravitational interaction. We find a novel relation between mass of brane gauge field and the brane cosmological constant.Comment: 20 pages, LaTex 2e, revised version (to appear in Phys. Rev. D

Atypical coordination of cortical oscillations in response to speech in autism.

Subjects with autism often show language difficulties, but it is unclear how they relate to neurophysiological anomalies of cortical speech processing. We used combined EEG and fMRI in 13 subjects with autism and 13 control participants and show that in autism, gamma and theta cortical activity do not engage synergistically in response to speech. Theta activity in left auditory cortex fails to track speech modulations, and to down-regulate gamma oscillations in the group with autism. This deficit predicts the severity of both verbal impairment and autism symptoms in the affected sample. Finally, we found that oscillation-based connectivity between auditory and other language cortices is altered in autism. These results suggest that the verbal disorder in autism could be associated with an altered balance of slow and fast auditory oscillations, and that this anomaly could compromise the mapping between sensory input and higher-level cognitive representations

Gravity of higher-dimensional global defects

Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the n extra dimensions. For Lambda = 0 and n > 2, the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Lambda > 0, one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For Lambda < 0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.Comment: 18 pages, no figures, uses revte

Gauge-invariant fluctuations of scalar branes

A generalization of the Bardeen formalism to the case of warped geometries is presented. The system determining the gauge-invariant fluctuations of the metric induced by the scalar fluctuations of the brane is reduced to a set of Schr\"odinger-like equations for the Bardeen potentials and for the canonical normal modes of the scalar-tensor action. Scalar, vector and tensor modes of the geometry are classified according to four-dimensional Lorentz transformations. While the tensor modes of the geometry live on the brane determining the corrections to Newton law, the scalar and and vector fluctuations exhibit non normalizable zero modes and are, consequently, not localized on the brane. The spectrum of the massive modes of the fluctuations is analyzed using supersymmetric quantum mechanics.Comment: 29 pages in Latex styl