Localization of 4D gravity on pure geometrical thick branes

Abstract

We consider the generation of thick brane configurations in a pure geometric Weyl integrable 5D spacetime 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 RandallSundrum (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 Z 2 -symmetry along the extra dimension which, indeed, can be either compact or extended, and supplements brane solutions previously found by other authors. In the noncompact case, this field configuration represents a thick brane with positive energy density centered at y c 2 , whereas pairs of thick branes arise in the compact case. Remarkably, the Weylian scalar curvature is nonsingular along the fifth dimension in the noncompact 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 c 2 and turn asymptotically into plane waves.

de Sitter thick brane solution in Weyl geometry

“…[14,35,36,37], the authors have studied brane world scenario in the frame of Weyl geometry, and achieved various solutions respected to Minkowski thick branes. For most of these branes [35,36], there exist a single bound state which represents a stable 4-dimensional graviton and the continuum spectrum of massive modes of KK excitations without mass gap for a volcano potential.…”

“…[14,35,36,37], the authors have studied brane world scenario in the frame of Weyl geometry, and achieved various solutions respected to Minkowski thick branes. For most of these branes [35,36], there exist a single bound state which represents a stable 4-dimensional graviton and the continuum spectrum of massive modes of KK excitations without mass gap for a volcano potential. While in [14], the KK spectrum is quantized for an infinite square-like potential wall, and in [37], there exist one massless bound state, one massive KK bound state and the delocalized continuum spectrum for a modified Pöschl-Teller potential.…”

“…[14,35,36,37], the authors studied thick brane solutions to the theory (2.1), and they considered the metric that respects four-dimensional Poincaré invariance:…”

“…More precisely, a Weyl geometry is an affine manifold specified by (g M N , ω), where g M N is the metric tensor and ω is the geometric scalar ω. Since a conformal transformation can map a Weyl manifold into a Riemann one, the particular type of gauge geometries is called conformally Weyl or Riemann integrable space-time [35]. On the other hand, Weyl integrable manifold is invariant under a Weyl rescaling (see, (2.2) for detail), when this invariance is broken, the Weyl scalar function ω transforms into an observable field which generates the smooth thick brane configurations.…”

Thick branes with inner structure in mimetic gravity

“…It is necessary to investigate thick brane in this theory. In the thick brane world scenario, the brane can be a domain wall generated by a background scalar field [37][38][39][53][54][55][56][57][58] or by pure geometry in a co-dimension one space-time [59][60][61][62][63]. On the other hand, it is shown that in some cases thick branes may have inner structure, which may lead to new phenomenon in the resonance and the localization of gravity and matter fields [64][65][66][67][68][69].…”