Dagoberto Malagon-Morejon

We investigate a cosmological solution within the framework of a 5D standing wave braneworld model generated by gravity coupled to a massless scalar phantom-like field. By obtaining a full exact solution of the model we found a novel dynamical mechanism in which the anisotropic nature of the primordial metric gives rise to i) inflation along certain spatial dimensions, and ii) deflation and a shrinking reduction of the number of spatial dimensions along other directions. This dynamical mechanism can be relevant for dimensional reduction in string and other higher dimensional theories in the attempt of getting a 4D isotropic expanding space-time.

We consider warped five-dimensional thick braneworlds with four-dimensional Poincar\'e invariance originated from bulk scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term. The background field equations as well as the perturbed equations are investigated. A relationship between 4D and 5D Planck masses is studied in general terms. By imposing finiteness of the 4D Planck mass and regularity of the geometry, the localization properties of the tensor modes of the perturbed geometry are analyzed to first order, for a wide class of solutions. In order to explore the gravity localization properties for this model, the normalizability condition for the lowest level of the tensor fluctuations is analyzed. It is found that for the examined class of solutions, gravity in 4 dimensions is recovered if the curvature invariants are regular and the 4D Planck mass is finite. It turns out that both the addition of the Gauss-Bonnet term and the non-minimal coupling between the scalar field and gravity {\it reduce} the value of the 4D Planck mass compared to its value when the scalar field and gravity are minimally coupled and the Gauss-Bonnet term is absent. The above discussed analysis depends on the explicit form of the scalar field (through its non-minimal coupling to gravity), making necessary the construction of explicit solutions in order to get results in closed form, and is illustrated with some examples which constitute smooth generalizations of the so-called Randall-Sundrum braneworld model. These solutions were obtained by making use of a detailed {\it singular perturbation theory} procedure with respect to the non-minimal coupling parameter between the scalar field and gravity, a difficult task that we managed to perform in such a way that all the physically meaningful conditions for the localization of gravity are fully satisfied. From the obtained...

We present a consistent derivation of the recently proposed 5D anisotropic standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We explicitly solve the corresponding junction conditions, a fact that enables us to give a physical interpretation to the anisotropic energy-momentum tensor components on the brane. So matter on the brane represents an oscillating fluid which emits anisotropic waves into the bulk. We also analyze the Sturm-Liouville problem associated to the correct localization condition of the transverse to the brane metric and scalar fields. It is shown that this condition restricts the physically meaningful space of solutions for the localization of the fluctuations of the model.

In this work we present a simple thick braneworld model that is generated by an intriguing interplay between a 5D cosmological constant with a de Sitter metric induced in the 3-brane without the inclusion of scalar fields. We show that 4D gravity is localized on this brane, provide analytic expressions for the massive Kaluza-Klein (KK) fluctuation modes and also show that the spectrum of metric excitations displays a mass gap. We finally present the corrections to Newton's law due to these massive modes. This model has no naked singularities along the fifth dimension despite the existence of a mass gap in the graviton spectrum as it happens in thick branes with 4D Poincare symmetry, providing a simple model with very good features: the curvature is completely smooth along the fifth dimension, it localizes 4D gravity and the spectrum of gravity fluctuations presents a mass gap, a fact that rules out the existence of phenomenologically dangerous ultralight KK excitations in the model. We finally present our solution as a limit of scalar thick branes.

We review some interrelated aspects of thick brane worlds constructed within the framework of 5D gravity coupled to a scalar field depending on the extra dimension. It turns out that when analyzing localization of 4D gravity in this smooth version of the Randall-Sundrum model, a kind of dichotomy emerges. In the first case the geometry is completely smooth and the spectrum of metric fluctuations shows a single massless bound state, corresponding to the 4D graviton, and a tower of massive states described by a continuous spectrum of Kaluza-Klein excitations starting from zero mass, indicating the lack of a mass gap. In the second case, there are two bound states, a massless 4D graviton and a massive excitation, separated by a mass gap from a continuous spectrum of massive modes; nevertheless, the presence of a mass gap in the graviton spectrum of the theory is responsible for a naked singularity at the boundaries (or spatial infinity) of the Riemannian manifold. However, the imposition of unitary boundary conditions, which is equivalent to eliminating the continuous spectrum of gravitational massive modes, renders these singularities harmless from the physical point of view, providing the viability of the model.