6 research outputs found
Instability of brane cosmological solutions with flux compactifications
We discuss the stability of the higher-dimensional de Sitter (dS) brane
solutions with two-dimensional internal space in the Einstein-Maxwel theory. We
show that an instability appears in the scalar-type perturbations with respect
to the dS spacetime. We derive a differential relation which has the very
similar structure to the ordinary laws of thermodynamics as an extension of the
work for the six-dimensional model [20]. In this relation, the area of dS
horizon (integrated over the two internal dimensions) exactly behaves as the
thermodynamical entropy. The dynamically unstable solutions are in the
thermodynamically unstable branch. An unstable dS compactification either
evolves toward a stable configuration or two-dimensional internal space is
decompactified. These dS brane solutions are equivalent to the accelerating
cosmological solutions in the six-dimensional Einstein-Maxwell-dilaton theory
via dimensional reduction. Thus, if the seed higher-dimensional solution is
unstable, the corresponding six-dimensional solution is also unstable. From the
effective four-dimensional point of view, a cosmological evolution from an
unstable cosmological solution in higher dimensions may be seen as a process of
the transition from the initial cosmological inflation to the current dark
energy dominated Universe.Comment: 11 pages, 3 figures, references added, to appear in CQ
Brane-bulk matter relation for a purely conical codimension-2 brane world
We study gravity on an infinitely thin codimension-2 brane world, with purely
conical singularities and in the presence of an induced gravity term on the
brane. We show that in this approximation, the energy momentum tensor of the
bulk is strongly related to the energy momentum tensor of the brane and thus
the gravity dynamics on the brane are induced by the bulk content. This is in
contrast with the gravity dynamics on a codimension-1 brane. We show how this
strong result is relaxed after including a Gauss-Bonnet term in the bulk.Comment: 12 pages, mistake corrected, references adde
Cosmological Evolution of a Purely Conical Codimension-2 Brane World
We study the cosmological evolution of isotropic matter on an infinitely thin
conical codimension-two brane-world. Our analysis is based on the boundary
dynamics of a six-dimensional model in the presence of an induced gravity term
on the brane and a Gauss-Bonnet term in the bulk. With the assumption that the
bulk contains only a cosmological constant Lambda_B, we find that the isotropic
evolution of the brane-universe imposes a tuned relation between the energy
density and the brane equation of state. The evolution of the system has fixed
points (attractors), which correspond to a final state of radiation for
Lambda_B=0 and to de Sitter state for Lambda_B>0. Furthermore, considering
anisotropic matter on the brane, the tuning of the parameters is lifted, and
new regions of the parametric space are available for the cosmological
evolution of the brane-universe. The analysis of the dynamics of the system
shows that, the isotropic fixed points remain attractors of the system, and for
values of Lambda_B which give acceptable cosmological evolution of the equation
of state, the line of isotropic tuning is a very weak attractor. The initial
conditions, in this case, need to be fine tuned to have an evolution with
acceptably small anisotropy.Comment: 20 pages, 4 figures, typo correcte
Conservation equation on braneworlds in six dimensions
We study braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. The
Gauss-Bonnet term is crucial for the equations to be well-posed in six
dimensions when non-trivial matter on the brane is included (the also involved
induced gravity term is not significant for their structure), and the matching
conditions of the braneworld are known. We show that the energy-momentum of the
brane is always conserved, independently of any regular bulk energy-momentum
tensor, contrary to the situation of the five-dimensional case.Comment: References added, minor changes, 3 pages, RevTeX, to app. in Class.
Quant. Gra
Low energy effective theory on a regularized brane in 6D gauged chiral supergravity
We derive the low energy effective theory on a brane in six-dimensional
chiral supergravity. The conical 3-brane singularities are resolved by
introducing cylindrical codimension one 4-branes whose interiors are capped by
a regular spacetime. The effective theory is described by the Brans-Dicke (BD)
theory with the BD parameter given by . The BD field is
originated from a modulus which is associated with the scaling symmetry of the
system. If the dilaton potentials on the branes preserve the scaling symmetry,
the scalar field has an exponential potential in the Einstein frame. We show
that the time dependent solutions driven by the modulus in the four-dimensional
effective theory can be lifted up to the six-dimensional exact solutions found
in the literature. Based on the effective theory, we discuss a possible way to
stabilize the modulus to recover standard cosmology and also study the
implication for the cosmological constant problem.Comment: 12 pages, 1 figur
Brane-World Gravity
The observable universe could be a 1+3-surface (the "brane") embedded in a
1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model
particles and fields trapped on the brane while gravity is free to access the
bulk. At least one of the \textit{d} extra spatial dimensions could be very
large relative to the Planck scale, which lowers the fundamental gravity scale,
possibly even down to the electroweak ( TeV) level. This revolutionary
picture arises in the framework of recent developments in M theory. The
1+10-dimensional M theory encompasses the known 1+9-dimensional superstring
theories, and is widely considered to be a promising potential route to quantum
gravity. At low energies, gravity is localized at the brane and general
relativity is recovered, but at high energies gravity "leaks" into the bulk,
behaving in a truly higher-dimensional way. This introduces significant changes
to gravitational dynamics and perturbations, with interesting and potentially
testable implications for high-energy astrophysics, black holes, and cosmology.
Brane-world models offer a phenomenological way to test some of the novel
predictions and corrections to general relativity that are implied by M theory.
This review analyzes the geometry, dynamics and perturbations of simple
brane-world models for cosmology and astrophysics, mainly focusing on warped
5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover
the simplest brane-world models in which 4-dimensional gravity on the brane is
modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati
models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004)
"Brane-World Gravity", 119 pages, 28 figures, the update contains new
material on RS perturbations, including full numerical solutions of
gravitational waves and scalar perturbations, on DGP models, and also on 6D
models. A published version in Living Reviews in Relativit