87 research outputs found
(1+3) Covariant Dynamics of Scalar Perturbations in Braneworlds
We discuss the dynamics of linear, scalar perturbations in an almost
Friedmann-Robertson-Walker braneworld cosmology of Randall-Sundrum type II
using the 1+3 covariant approach. We derive a complete set of frame-independent
equations for the total matter variables, and a partial set of equations for
the non-local variables which arise from the projection of the Weyl tensor in
the bulk. The latter equations are incomplete since there is no propagation
equation for the non-local anisotropic stress. We supplement the equations for
the total matter variables with equations for the independent constituents in a
cold dark matter cosmology, and provide solutions in the high and low-energy
radiation-dominated phase under the assumption that the non-local anisotropic
stress vanishes. These solutions reveal the existence of new modes arising from
the two additional non-local degrees of freedom. Our solutions should prove
useful in setting up initial conditions for numerical codes aimed at exploring
the effect of braneworld corrections on the cosmic microwave background (CMB)
power spectrum. As a first step in this direction, we derive the covariant form
of the line of sight solution for the CMB temperature anisotropies in
braneworld cosmologies, and discuss possible mechanisms by which braneworld
effects may remain in the low-energy universe.Comment: 22 pages replaced with additional references and minor corrections in
Revtex4, and accepted for publication in Phys. Rev.
Quantum fluctuations in brane-world inflation without inflaton on the brane
A Randall-Sundrum type brane-cosmological model in which slow-roll inflation
on the brane is driven solely by a bulk scalar field was recently proposed by
Himemoto and Sasaki. We analyze their model in detail and calculate the quantum
fluctuations of the bulk scalar field with . We decompose
the bulk scalar field into the infinite mass spectrum of 4-dimensional fields;
the field with the smallest mass-square, called the zero-mode, and the
Kaluza-Klein modes above it with a mass gap. We find the zero-mode dominance of
the classical solution holds if , where is
the curvature radius of the effectively anti-de Sitter bulk, but it is violated
if , though the violation is very small. Then we evaluate
the vacuum expectation value on the brane. We find the
zero-mode contribution completely dominates if similar
to the case of classical background. In contrast, we find the Kaluza-Klein
contribution is small but non-negligible if the value of is
large.Comment: 12pages, 1 figure, typos corrected, a couple of paragraphs modified
but no major change in the text, final version to be published in PR
Godel brane
We consider the brane-world generalisation of the Godel universe and analyse
its dynamical interaction with the bulk. The exact homogeneity of the standard
Godel spacetime no longer holds, unless the bulk is also static. We show how
the anisotropy of the Godel-type brane is dictated by that of the bulk and find
that the converse is also true. This determines the precise evolution of the
nonlocal anisotropic stresses, without any phenomenological assumptions, and
leads to a self-consistent closed set of equations for the evolution of the
Godel brane. We also examine the causality of the Godel brane and show that the
presence of the bulk cannot prevent the appearance of closed timelike curves.Comment: Revised version, to match paper published in Phys. Rev.
On Brane World Cosmological Perturbations
We discuss the scalar cosmological perturbations in a 3-brane world with a 5D
bulk. We first show explicitly how the effective perturbed Einstein's equations
on the brane (involving the Weyl fluid) are encoded into Mukohyama's master
equation. We give the relation between Mukohyama's master variable and the
perturbations of the Weyl fluid, we also discuss the relation between the
former and the perturbations of matter and induced metric on the brane. We show
that one can obtain a boundary condition on the brane for the master equation
solely expressible in term of the master variable, in the case of a perfect
fluid with adiabatic perturbations on a Randall-Sundrum (RS) or
Dvali-Gabadadze-Porrati (DGP) brane. This provides an easy way to solve
numerically for the evolution of the perturbations as well as should shed light
on the various approximations done in the literature to deal with the Weyl
degrees of freedom.Comment: 36 pages, 1 figur
Exactly solvable model for cosmological perturbations in dilatonic brane worlds
We construct a model where cosmological perturbations are analytically solved
based on dilatonic brane worlds. A bulk scalar field has an exponential
potential in the bulk and an exponential coupling to the brane tension. The
bulk scalar field yields a power-law inflation on the brane. The exact
background metric can be found including the back-reaction of the scalar field.
Then exact solutions for cosmological perturbations which properly satisfy the
junction conditions on the brane are derived. These solutions provide us an
interesting model to understand the connection between the behavior of
cosmological perturbations on the brane and the geometry of the bulk. Using
these solutions, the behavior of an anisotropic stress induced on the
inflationary brane by bulk gravitational fields is investigated.Comment: 30 pages, typos corrected, reference adde
Perturbations on a moving D3-brane and mirage cosmology
We study the evolution of perturbations on a moving probe D3-brane coupled to
a 4-form field in an AdS-Schwarzschild bulk. The unperturbed dynamics are
parametrised by a conserved energy and lead to Friedmann-Robertson-Walker
`mirage' cosmology on the brane with scale factor . The fluctuations
about the unperturbed worldsheet are then described by a scalar field
. We derive an equation of motion for , and find that
in certain regimes of the effective mass squared is negative. On an
expanding BPS brane with E=0 superhorizon modes grow as whilst subhorizon
modes are stable. When the brane contracts, all modes grow. We also briefly
discuss the case when , BPS anti-branes as well as non-BPS branes.
Finally, the perturbed brane embedding gives rise to scalar perturbations in
the FRW universe. We show that is proportional to the gauge invariant
Bardeen potentials on the brane.Comment: 26 pages, 5 figures, to appear in Phys.Rev.D, comments and minor
corrections adde
Radion and Holographic Brane Gravity
The low energy effective theory for the Randall-Sundrum two brane system is
investigated with an emphasis on the role of the non-linear radion in the brane
world. The equations of motion in the bulk is solved using a low energy
expansion method. This allows us, through the junction conditions, to deduce
the effective equations of motion for the gravity on the brane. It is shown
that the gravity on the brane world is described by a quasi-scalar-tensor
theory with a specific coupling function omega(Psi) = 3 Psi / 2(1-Psi) on the
positive tension brane and omega(Phi) = -3 Phi / 2(1+Phi) on the negative
tension brane, where Psi and Phi are non-linear realizations of the radion on
the positive and negative tension branes, respectively. In contrast to the
usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two
kinds of matter, namely, the matters on both positive and negative tension
branes, with different effective gravitational coupling constants. In
particular, the radion disguised as the scalar fields Psi and Phi couples with
the sum of the traces of the energy momentum tensor on both branes. In the
course of the derivation, it has been revealed that the radion plays an
essential role to convert the non-local Einstein gravity with the generalized
dark radiation to the local quasi-scalar-tensor gravity. For completeness, we
also derive the effective action for our theory by substituting the bulk
solution into the original action. It is also shown that the
quasi-scalar-tensor gravity works as holograms at the low energy in the sense
that the bulk geometry can be reconstructed from the solution of the
quasi-scalar-tensor gravity.Comment: Revtex4, 18 pages, revised version, conclusions unchanged, references
adde
Bulk Gravitational Field and Cosmological Perturbations on the Brane
We investigate the effect of the bulk gravitational field on the cosmological
perturbations on a brane embedded in the 5D Anti-de Sitter (AdS) spacetime. The
effective 4D Einstein equations for the scalar cosmological perturbations on
the brane are obtained by solving the perturbations in the bulk. Then the
behaviour of the corrections induced by the bulk gravitational field to the
conventional 4D Einstein equation are determined. Two types of the corrections
are found. First we investigate the corrections which become significant at
scales below the AdS curvature scales and in the high energy universe with the
energy density larger than the tension of the brane. The evolution equation for
the perturbations on the brane is found and solved. Another type of the
corrections is induced on the brane if we consider the bulk perturbations which
do not contribute to the metric perturbations but do contribute to the matter
perturbations. At low energies, they have imaginary mass m^2=-(2/3) \k^2 in
the bulk where \k is the 3D comoving wave number of the perturbations. They
diverge at the horizon of the AdS spacetime. The induced density perturbations
behave as sound waves with sound velocity in the low energy
universe. At large scales, they are homogeneous perturbations that depend only
on time and decay like radiation. They can be identified as the perturbations
of the dark radiation. They produce isocurvature perturbations in the matter
dominated era. Their effects can be observed as the shifts of the location and
the height of the acoustic peak in the CMB spectrum.Comment: 35 pages, 1 figur
Braneworld Tensor Anisotropies in the CMB
Cosmic microwave background (CMB) observations provide in principle a
high-precision test of models which are motivated by M theory. We set out the
framework of a program to compute the tensor anisotropies in the CMB that are
generated in braneworld models. In the simplest approximation, we show the
braneworld imprint as a correction to the power spectra for standard
temperature and polarization anisotropies.Comment: Minor corrections and references added. Accepted for publication in
Phys. Rev.
Brane World Effective Action at Low Energies and AdS/CFT Correspondence
A low energy iteration scheme to study nonlinear gravity in the brane world
is developed. As a result, we obtain the brane world effective action at low
energies. The relation between the geometrical approach and the approach using
the AdS/CFT correspondence is also clarified. In particular, we find
generalized dark radiation as homogeneous solutions in our iteration scheme.
Moreover, the precise correspondence between the bulk geometry and the brane
effective action is established, which gives a holographic view of the brane
world.Comment: Revtex4, 12 pages, references added. Version accepted for publicaton
in Phys. Rev.
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