4D gravity localized in non Z_2-symmetric thick branes

We present a comparative analysis of localization of 4D gravity on a non Z_2-symmetric scalar thick brane in both a 5-dimensional Riemannian space time and a pure geometric Weyl integrable manifold. This work was mainly motivated by the hypothesis which claims that Weyl geometries mimic quantum behaviour classically. We start by obtaining a classical 4-dimensional Poincare invariant thick brane solution which does not respect Z_2-symmetry along the (non-)compact extra dimension. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y_0. The only qualitative difference we have encountered when comparing both frames is that the scalar curvature of the Riemannian manifold turns out to be singular for the found solution, whereas its Weylian counterpart presents a regular behaviour. By studying the transverse traceless modes of the fluctuations of the classical backgrounds, we recast their equations into a Schroedinger's equation form with a volcano potential of finite bottom (in both frames). By solving the Schroedinger equation for the massless zero mode m^2=0 we obtain a single bound state which represents a stable 4-dimensional graviton in both frames. We also get a continuum gapless spectrum of KK states with positive m^2>0 that are suppressed at y_0, turning into continuum plane wave modes as "y" approaches spatial infinity. We show that for the considered solution to our setup, the potential is always bounded and cannot adopt the form of a well with infinite walls; thus, we do not get a discrete spectrum of KK states, and we conclude that the claim that Weylian structures mimic, classically, quantum behaviour does not constitute a generic feature of these geometric manifolds.Comment: 13 pages, 4 figures, JHEP forma

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.Comment: 25 pages in latex, no figures, content changed, corrections to Newton's law included for smooth version of RS model and an author adde

Gravedad tetradimensional localizada en membranas anchas sin simetría Z2

El trabajo que se presenta en esta tesis es un análisis comparativo de la localización de la gravedad tetradimensional en una membrana ancha que carece de la simetría de reflexión (y ?? -y), mejor conocida como simetría Z2 , en dos marcos diferentes: un espacio tiempo pentadimensional riemanniano y una variedad integrable de Weyl puramente geométrica. La posibilidad de que el espacio tiempo en que vivimos tenga más de tres dimensiones espaciales ha sido motivo de controversias, discusiones, investigaciones y también de resultados interesantes que pueden dar respuesta a algunos problemas relevantes de la física de altas energías tales como el de la constante cosmológica, la materia obscura, el problema de la jerarquía de masas, entre otros. Una de las principales motivaciones para considerar un espacio con dimensiones extra consiste en que la mayoría de las teorías que incluyen de manera consistente la gravedad tetradimensional (mejor conocidas como teorías de unificación), están formuladas de manera natural (o consistente) en espacios tiempo con más de cuatro dimensiones. Sin embargo, paralelamente a estas formulaciones teóricas, las líneas de investigación fenomenológicas nos llevan a tener una mejor comprensión de cómo se pueden manifestar estas dimensiones y si pueden o no manifestarse, del mismo modo que nos muestran si son o no de ayuda para dar una explicación a los problemas que presenta la física moderna