378 research outputs found
Diagrammatic Derivation of Lovelock Densities
We discuss a method of calculating the various scalar densities encountered
in Lovelock theory which relies on diagrammatic, instead of algebraic
manipulations. Taking advantage of the known symmetric and antisymmetric
properties of the Riemann tensor which appears in the Lovelock densities, we
map every quadratic or higher contraction into a corresponding permutation
diagram. The derivation of the explicit form of each density is then reduced to
identifying the distinct diagrams, from which we can also read off the overall
combinatoric factors. The method is applied to the first Lovelock densities, of
order two (Gauss-Bonnet term) and three.Comment: 5 pages, 4 figures. References added. Corrected minor typo
Cosmic Acceleration Data and Bulk-Brane Energy Exchange
We consider a braneworld model with bulk-brane energy exchange. This allows
for crossing of the w=-1 phantom divide line without introducing phantom energy
with quantum instabilities. We use the latest SnIa data included in the Gold06
dataset to provide an estimate of the preferred parameter values of this
braneworld model. We use three fitting approaches which provide best fit
parameter values and hint towards a bulk energy component that behaves like
relativistic matter which is propagating in the bulk and is moving at a speed v
along the fifth dimension, while the bulk-brane energy exchange component
corresponds to negative pressure and signifies energy flowing from the bulk
into the brane. We find that the best fit effective equation of state parameter
marginally crosses the phantom divide line w=-1. Thus, we have
demonstrated both the ability of this class of braneworld models to provide
crossing of the phantom divide and also that cosmological data hint towards
natural values for the model parameters.Comment: 12 pages, 2 figures, added comments, references update
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
Brane Cosmology with a Non-Minimally Coupled Bulk-Scalar Field
We consider the cosmological evolution of a brane in the presence of a bulk
scalar field coupled to the Ricci scalar through a term f(\phi)R. We derive the
generalized Friedmann equation on the brane in the presence of arbitrary brane
and bulk-matter, as well as the scalar field equation, allowing for a general
scalar potential V(phi). We focus on a quadratic form of the above non-minimal
coupling and obtain a class of late-time solutions for the scale factor and the
scalar field on the brane that exhibit accelerated expansion for a range of the
non-minimal coupling parameter.Comment: 15 page
Synergistic Gravity and the Role of Resonances in GRS-Inspired Braneworlds
We consider 5D braneworld models of quasi-localized gravity in which 4D
gravity is reproduced at intermediate scales while the extra dimension opens up
at both the very short and the very long distances, where the geometry is flat.
Our main interest is the interplay between the zero mode of these models,
whenever a normalizable zero mode exists, and the effects of zero energy
graviton resonant modes coming from the contributions of massive KK modes. We
first consider a compactified version of the GRS model and find that
quasi-localized gravity is characterized by a scale for which both the
resonance and the zero mode have significant contribution to 4D gravity. Above
this scale, gravity is primarily mediated by the zero mode, while the resonance
gives only minor corrections. Next, we consider an asymmetric version of the
standard non-compact GRS model, characterized by different cosmological
constants on each AdS side. We show that a resonance is present but the
asymmetry, through the form of the localizing potential, can weaken it,
resulting in a shorter lifetime and, thus, in a shorter distance scale for 4D
gravity. As a third model exhibiting quasi-localization, we consider a version
of the GRS model in which the central positive tension brane has been replaced
by a configuration of a scalar field propagating in the bulk.Comment: 18 pages, 3 figures, added 1 figure, revised version as published in
Class. Quant. Gra
Braneworld models with a non-minimally coupled phantom bulk field: a simple way to obtain the -1-crossing at late times
We investigate general braneworld models, with a non-minimally coupled
phantom bulk field and arbitrary brane and bulk matter contents. We show that
the effective dark energy of the brane-universe acquires a dynamical nature, as
a result of the non-minimal coupling which provides a mechanism for an indirect
"bulk-brane interaction" through gravity. For late-time cosmological evolution
and without resorting to special ansatzes or to specific areas of the parameter
space, we show that the -1-crossing of its equation-of-state parameter is
general and can be easily achieved. As an example we provide a simple, but
sufficiently general, approximate analytical solution, that presents the
crossing behavior.Comment: 11 pages, 2 figure
The phase portrait of a matter bounce in Horava-Lifshitz cosmology
The occurrence of a bounce in FRW cosmology requires modifications of general
relativity. An example of such a modification is the recently proposed
Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term
with a negative coefficient in the analog of the Friedmann equation. This paper
describes a phase space analysis of models of this sort with the aim of
determining to what extent bouncing solutions can occur. A simplification,
valid in the relevant region, allows a reduction of the dimension of phase
space so that visualization in three dimensions is possible. It is found that a
bounce is possible, but not generic in models under consideration. Apart from
previously known bouncing solutions some new ones are also described. Other
interesting solutions found include ones which describe a novel sort of
oscillating universes.Comment: 14 pages, 8 figure
Remarks on the Scalar Graviton Decoupling and Consistency of Horava Gravity
Recently Horava proposed a renormalizable gravity theory with higher
derivatives by abandoning the Lorenz invariance in UV. But there have been
confusions regarding the extra scalar graviton mode and the consistency of the
Horava model. I reconsider these problems and show that, in the Minkowski
vacuum background, the scalar graviton mode can be consistency decoupled from
the usual tensor graviton modes by imposing the (local) Hamiltonian as well as
the momentum constraints.Comment: Some clarifications regarding the projectable case added, Typos
corrected, Comments (Footnote No.9, Note Added) added, References updated,
Accepted in CQ
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