43 research outputs found
Localizing gravity on thick branes: a solution for massive KK modes of the Schroedinger equation
We generate scalar thick brane configurations in a 5D Riemannian space time
which describes gravity coupled to a self-interacting scalar field. We also
show that 4D gravity can be localized on a thick brane which does not
necessarily respect Z_2-symmetry, generalizing several previous models based on
the Randall-Sundrum system and avoiding the restriction to orbifold geometries
as well as the introduction of the branes in the action by hand. We begin by
obtaining a smooth brane configuration that preserves 4D Poincar'e invariance
and violates reflection symmetry along the fifth dimension. The extra dimension
can have either compact or extended topology, depending on the values of the
parameters of the solution. In the non-compact case, our field configuration
represents a thick brane with positive energy density centered at y=c_2,
whereas in the compact case we get pairs of thick branes. We recast as well the
wave equations of the transverse traceless modes of the linear fluctuations of
the classical solution into a Schroedinger's equation form with a volcano
potential of finite bottom. We solve Schroedinger equation for the massless
zero mode m^2=0 and obtain a single bound wave function which represents a
stable 4D graviton and is free of tachyonic modes with m^2<0. We also get a
continuum spectrum of Kaluza-Klein (KK) states with m^2>0 that are suppressed
at y=c_2 and turn asymptotically into plane waves. We found a particular case
in which the Schroedinger equation can be solved for all m^2>0, giving us the
opportunity of studying analytically the massive modes of the spectrum of KK
excitations, a rare fact when considering thick brane configurations.Comment: 8 pages in latex. We corrected signs in the field equations, the
expressions for the scalar field and the self-interacting potential. Due to
the fact that no changes are introduced in the warp factor, the physics of
the system remains the sam
Mass gap for gravity localized on Weyl thick branes
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
Localization of gravity on a de Sitter thick braneworld without scalar fields
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.Comment: 11 pages in latex, no figures, title and abstract changed, a new
section and some references adde
de Sitter Thick Brane Solution in Weyl Geometry
In this paper, we consider a de Sitter thick brane model in a pure geometric
Weyl integrable five-dimensional space-time, which is a generalization of
Riemann geometry and is invariant under a so-called Weyl rescaling. We find a
solution of this model via performing a conformal transformation to map the
Weylian structure into a familiar Riemannian one with a conformal metric. The
metric perturbations of the model are discussed. For gravitational
perturbation, we get the effective modified Pschl-Teller
potential in corresponding Schrdinger equation for
Kaluza-Klein (KK) modes of the graviton. There is only one bound state, which
is a normalizable massless zero mode and represents a stable 4-dimensional
graviton. Furthermore, there exists a mass gap between the massless mode and
continuous KK modes. We also find that the model is stable under the scalar
perturbation in the metric. The correction to the Newtonian potential on the
brane is proportional to , where is the de Sitter
parameter of the brane. This is very different from the correction caused by a
volcano-like effective potential.Comment: 24 pages, 13 figures, published versio
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
Effective Monopoles within Thick Branes
The monopole mass is revealed to be considerably modified in the thick
braneworld paradigm, and depends on the position of the monopole in the brane
as well. Accordingly, the monopole radius continuously increases, leading to an
unacceptable setting that can be circumvented when the brane thickness has an
upper limit. Despite such peculiar behavior, the quantum corrections accrued --
involving the classical monopole solution -- are shown to be still under
control. We analyze the monopole's peculiarities also taking into account the
localization of the gauge fields. Furthermore, some additional analysis in the
thick braneworld context and the similar behavior evinced by the topological
string are investigated.Comment: 7 pages, 1 figur
Thick brane in 7D and 8D spacetimes
We consider a thick brane model supported by two interacting scalar fields in
7D and 8D general relativity. Using the special type of a potential energy, we
obtain numerically the regular asymptotically flat vacuum solutions. A
possibility of obtaining the similar solutions for an arbitrary number of the
extra spatial dimensions is estimated.Comment: 3 Ref's are adde