7,745 research outputs found
Quantization of scalar perturbations in brane-world inflation
We consider a quantization of scalar perturbations about a de Sitter brane in
a 5-dimensional anti-de Sitter (AdS) bulk spacetime. We first derive the second
order action for a master variable for 5-dimensional gravitational
perturbations. For a vacuum brane, there is a continuum of normalizable
Kaluza-Klein (KK) modes with . There is also a light radion mode with
which satisfies the junction conditions for two branes, but is
non-normalizable for a single brane model. We perform the quantization of these
bulk perturbations and calculate the effective energy density of the projected
Weyl tensor on the barne. If there is a test scalar field perturbation on the
brane, the mode together with the zero-mode and an infinite ladder
of discrete tachyonic modes become normalizable in a single brane model. This
infinite ladder of discrete modes as well as the continuum of KK modes with
introduce corrections to the scalar field perturbations at first-order
in a slow-roll expansion. We derive the second order action for the
Mukhanov-Sasaki variable coupled to the bulk perturbations which is needed to
perform the quantization and determine the amplitude of scalar perturbations
generated during inflation on the brane.Comment: 14 page
Numerical study of curvature perturbations in a brane-world inflation at high-energies
We study the evolution of scalar curvature perturbations in a brane-world
inflation model in a 5D Anti-de Sitter spacetime. The inflaton perturbations
are confined to a 4D brane but they are coupled to the 5D bulk metric
perturbations. We numerically solve full coupled equations for the inflaton
perturbations and the 5D metric perturbations using Hawkins-Lidsey inflationary
model. At an initial time, we assume that the bulk is unperturbed. We find that
the inflaton perturbations at high energies are strongly coupled to the bulk
metric perturbations even on subhorizon scales, leading to the suppression of
the amplitude of the comoving curvature perturbations at a horizon crossing.
This indicates that the linear perturbations of the inflaton field does not
obey the usual 4D Klein-Gordon equation due to the coupling to 5D gravitational
field on small scales and it is required to quantise the coupled brane-bulk
system in a consistent way in order to calculate the spectrum of the scalar
perturbations in a brane-world inflation.Comment: 16 pages, 5 figure
Quantum-mechanical generation of gravitational waves in braneworld
We study the quantum-mechanical generation of gravitational waves during
inflation on a brane embedded in a five-dimensional anti-de Sitter bulk. To
make the problem well-posed, we consider the setup in which both initial and
final phases are given by a de Sitter brane with different values of the Hubble
expansion rate. Assuming that the quantum state is in a de Sitter invariant
vacuum in the initial de Sitter phase, we numerically evaluate the amplitude of
quantum fluctuations of the growing solution of the zero mode in the final de
Sitter phase. We find that the vacuum fluctuations of the initial Kaluza-Klein
gravitons as well as of the zero mode gravitons contribute to the final
amplitude of the zero mode on small scales, and the power spectrum is quite
well approximated by what we call the rescaled spectrum, which is obtained by
rescaling the standard four-dimensional calculation following a simple mapping
rule. Our results confirm the speculation raised in Ref.
\cite{Kobayashi:2003cn} before.Comment: 11 pages, 11 figure
Quasi Non-linear Evolution of Stochastic Bias
It is generally believed that the spatial distribution of galaxies does not
trace that of the total mass. The understanding of the bias effect is therefore
necessary to determine the cosmological parameters and the primordial density
fluctuation spectrum from the galaxy survey. The deterministic description of
bias may not be appropriate because of the various stochasticity of galaxy
formation process. In nature, the biasing is epoch dependent and recent deep
survey of the galaxy shows the large biasing at high redshift. Hence, we
investigate quasi non-linear evolution of the stochastic bias by using the tree
level perturbation method. Especially, the influence of the initial cross
correlation on the evolution of the skewness and the bi-spectrum is examined in
detail. We find that the non-linear bias can be generated dynamically. The
small value of the initial cross correlation can bend the \dg-\dm relation
effectively and easily lead to the negative curvature (). We also
propose a method to predict the bias, cross correlation and skewness at high
redshift. As an illustration, the possibility of the large biasing at high
redshift is discussed. Provided the present bias parameter as and
, we predict the large scale bias as at by fitting
the bi-spectrum to the Lick catalog data. Our results will be important for the
future deep sky survey.Comment: 20 pages, 5 Encapsulated Postscript figures, aastex, final version to
appear in Ap
Scalar perturbations in braneworld cosmology
We study the behaviour of scalar perturbations in the radiation-dominated era
of Randall-Sundrum braneworld cosmology by numerically solving the coupled bulk
and brane master wave equations. We find that density perturbations with
wavelengths less than a critical value (set by the bulk curvature length) are
amplified during horizon re-entry. This means that the radiation era matter
power spectrum will be at least an order of magnitude larger than the
predictions of general relativity (GR) on small scales. Conversely, we
explicitly confirm from simulations that the spectrum is identical to GR on
large scales. Although this magnification is not relevant for the cosmic
microwave background or measurements of large scale structure, it will have
some bearing on the formation of primordial black holes in Randall-Sundrum
models.Comment: 17 pages, 7 figure
Scalar cosmological perturbations in the Gauss-Bonnet braneworld
We study scalar cosmological perturbations in a braneworld model with a bulk
Gauss-Bonnet term. For an anti-de Sitter bulk, the five-dimensional
perturbation equations share the same form as in the Randall-Sundrum model,
which allows us to obtain metric perturbations in terms of a master variable.
We derive the boundary conditions for the master variable from the generalized
junction conditions on the brane. We then investigate several limiting cases in
which the junction equations are reduced to a feasible level. In the low energy
limit, we confirm that the standard result of four-dimensional Einstein gravity
is reproduced on large scales, whereas on small scales we find that the
perturbation dynamics is described by the four-dimensional Brans-Dicke theory.
In the high energy limit, all the non-local contributions drop off from the
junction equations, leaving a closed system of equations on the brane. We show
that, for inflation models driven by a scalar field on the brane, the
Sasaki-Mukhanov equation holds on the high energy brane in its original
four-dimensional form.Comment: 18 pages, v2: minor changes, reference added, v3: comments and
references added, accepted for publication in JCA
Slow-roll corrections to inflaton fluctuations on a brane
Quantum fluctuations of an inflaton field, slow-rolling during inflation are
coupled to metric fluctuations. In conventional four dimensional cosmology one
can calculate the effect of scalar metric perturbations as slow-roll
corrections to the evolution of a massless free field in de Sitter spacetime.
This gives the well-known first-order corrections to the field perturbations
after horizon-exit. If inflaton fluctuations on a four dimensional brane
embedded in a five dimensional bulk spacetime are studied to first-order in
slow-roll then we recover the usual conserved curvature perturbation on
super-horizon scales. But on small scales, at high energies, we find that the
coupling to the bulk metric perturbations cannot be neglected, leading to a
modified amplitude of vacuum oscillations on small scales. This is a large
effect which casts doubt on the reliability of the usual calculation of
inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure
Slow-roll corrections to inflaton fluctuations on a brane
Quantum fluctuations of an inflaton field, slow-rolling during inflation are
coupled to metric fluctuations. In conventional four dimensional cosmology one
can calculate the effect of scalar metric perturbations as slow-roll
corrections to the evolution of a massless free field in de Sitter spacetime.
This gives the well-known first-order corrections to the field perturbations
after horizon-exit. If inflaton fluctuations on a four dimensional brane
embedded in a five dimensional bulk spacetime are studied to first-order in
slow-roll then we recover the usual conserved curvature perturbation on
super-horizon scales. But on small scales, at high energies, we find that the
coupling to the bulk metric perturbations cannot be neglected, leading to a
modified amplitude of vacuum oscillations on small scales. This is a large
effect which casts doubt on the reliability of the usual calculation of
inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure
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