Alfredo Herrera-Aguilar

4D gravity localized in non Bbb Z2 -symmetric thick branes

We present a comparative analysis of localization of 4D gravity on a non 2 -symmetric scalar thick brane in both a 5-dimensional riemannian space time and a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. 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 Poincar? invariant thick brane solution which does not respect 2 -symmetry along the (non-)compact extra dimension. This field configuration reproduces the 2 -symmetric solutions previously found in the literature, in both the Riemann and the Weyl frames, when the parameter k 1 = 1. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y 0 . Thus, our field configurations can be compared with the standard Randall-Sundrum thin brane case. 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 Sch?dingers equation form with a volcano potential of finite bottom (in both frames). By solving the Sch?dinger 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 0

Localization of gravity on a de Sitter thick braneworld without scalar fields

> 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.

An anisotropic standing wave braneworld and associated Sturm?Liouville problem

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 Poincaré 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.

Aspects of thick brane worlds: 4D gravity localization, smoothness, and mass gap

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 of 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 with 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.

MATRIX ERNST POTENTIALS AND ORTHOGONAL SYMMETRY OF LOW ENERGY HETEROTIC STRING THEORY REDUCED TO THREE DIMENSIONS

We review some interrelated aspects of thick braneworlds 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 the transverse traceless modes of the 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.

Localization of gauge fields in a tachyonic de Sitter thick braneworld

A new coset matrix for low-energy limit of heterotic string theory reduced to three dimensions is constructed. The pair of matrix Ernst potentials uniquely connected with the coset matrix is derived. The action of the symmetry group on the Ernst potentials is established.

Charging symmetries and linearizing potentials for Einstein-Maxwell dilaton - axion theory

In this work we show that universal gauge vector fields can be localized on the recently proposed 5D thick tachyonic braneworld which involves a de Sitter cosmological background induced on the 3-brane. Namely, by performing a suitable decomposition of the vector field, the resulting 4D effective action corresponds to a massive gauge field, while the profile along the extra dimension obeys a Schrödinger-like equation with a Pöschl–Teller potential. It turns out that the massless zero mode of the gauge field is bound to the expanding 3-brane and allows us to recover the standard 4D electromagnetic phenomena of our world. Moreover, this zero mode is separated from the continuum of Kaluza–Klein (KK) modes by a mass gap determined by the scale of the expansion parameter. We also were able to analytically solve the corresponding Schrödinger-like equation for arbitrary mass, showing that KK massive modes asymptotically behave like plane waves, as expected.

Thick braneworlds generated by a non-minimally coupled scalar field and a Gauss–Bonnet term: conditions for the localization of gravity

We derive a set of complex potentials which linearize the action of charging symmetries of the stationary Einstein–Maxwell dilaton–axion theory.

Testing Hybrid Natural Inflation with BICEP2

We consider warped five-dimensional thick braneworlds with four-dimensional Poincare 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 analysed 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 analysed. It is found that for the examined class of solutions, gravity in four 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 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 obtain 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 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 explicit solutions, we found an interesting effect: when we consider a non-minimally coupled scalar–tensor theory, there arise solutions for which the symmetries of the background geometry are not preserved by the scalar matter energy density distribution. In particular, the value of the ‘5D cosmological constant’ of the asymptotically AdS5 spacetime (which is even with respect to the extra coordinate) gets different contributions at −∞ and +∞ from the asymptotic values of the self-interaction potential of the scalar field. Thus, an asymmetric energy density distribution of scalar matter gives rise to a spacetime which is completely even with respect to the fifth coordinate, in contrast to braneworld models derived from minimally coupled scalar–tensor theories, where both entities possess the same symmetry.

On localization of universal scalar fields in a tachyonic de Sitter thick braneworld

We analyse Hybrid Natural Inflation in view of the recent results for the tensor index reported by BICEP2. We find that it predicts a large running of the scalar spectrum which is potentially detectable by large scale structure through measurements of clustering of galaxies in combination with CMB data and by 21 cm forest observations. The running of the running is also relatively large becoming close to 10−2. Along the way, we find general consistency relations at which observables are subject if the slow-roll approximation is imposed. Failure to satisfy these equations by the values obtained for the observables in surveys would be a failure of the slow-roll approximation itself.