We present a comparative analysis of localization of 4D gravity on a non Z 2symmetric 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 Poincaré invariant thick brane solution which does not respect Z 2 -symmetry along the (non-)compact extra dimension. This field configuration reproduces the Z 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 Schödinger's equation form with a volcano potential of finite bottom (in both frames). By solving the Schödinger 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.

We study the properties of a previously found family of thick brane configurations in a pure geometric Weyl integrable 5D space time, a non-Riemannian generalization of Kaluza-Klein (KK) theory involving a geometric scalar field. Thus the 5D theory describes gravity coupled to a self-interacting scalar field which gives rise to the structure of the thick branes. Analyzing the graviton spectrum for this class of models, we find that a particularly interesting situation arises for a special case in which the 4D graviton is separated from the KK gravitons by a mass gap. The corresponding effective Schroedinger equation has a modified Poeschl-Teller potential and can be solved exactly. Apart from the massless 4D graviton, it contains one massive KK bound state, and the continuum spectrum of delocalized KK modes. We discuss the mass hierarchy problem, and explicitly compute the corrections to Newton's law in the thin brane limit.Comment: 6 pages in Revtex, no figures, journal version, significately revised and extende

We consider the generation of thick brane configurations in a pure geometric Weyl integrable 5D space time which constitutes a non-Riemannian generalization of Kaluza-Klein (KK) theory. In this framework, we show how 4D gravity can be localized on a scalar thick brane which does not necessarily respect reflection symmetry, generalizing in this way several previous models based on the Randall-Sundrum (RS) system and avoiding both, the restriction to orbifold geometries and the introduction of the branes in the action by hand. We first obtain a thick brane solution that preserves 4D Poincaré invariance and breaks Z2-symmetry along the extra dimension which, indeed, can be either compact or extended, and supplements brane solutions previously found by other authors. In the non-compact case, this field configuration represents a thick brane with positive energy density centered at y = c2, whereas pairs of thick branes arise in the compact case. Remarkably, the Weylian scalar curvature is non-singular along the fifth dimension in the non-compact case, in contraposition to the RS thin brane system. We also recast the wave equations of the transverse traceless modes of the linear fluctuations of the classical background into a Schrödinger's equation form with a volcano potential of finite bottom in both the compact and the extended cases. We solve Schrödinger equation for the massless zero mode m 2 = 0 and obtain a single bound wave function which represents a stable 4D graviton. We also get a continuum gapless spectrum of KK states with m 2 > 0 that are suppressed at y = c2 and turn asymptotically into plane waves.

We study tachyon inflation within the large-N formalism, which takes a prescription for the small Hubble flow slow-roll parameter ϵ1 as a function of the large number of e-folds N. This leads to a classification of models through their behaviour at large N. In addition to the perturbative N class, we introduce the polynomial and exponential classes for the ϵ1 parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for tachyon inflation. We also obtain new families of potentials from the polynomial class. We characterize the realizations of tachyon inflation by computing the usual cosmological observables up to second order in the Hubble flow slow-roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.