4,889 research outputs found
Self-accelerating universe in Galileon cosmology
We present a cosmological model with a solution that self-accelerates at late times without signs of ghost instabilities on small scales. The model is a natural extension of the Brans-Dicke (BD) theory including a nonlinear derivative interaction, which appears in a theory with the Galilean shift symmetry. The existence of the self-accelerating universe requires a negative BD parameter but, thanks to the nonlinear term, small fluctuations around the solution are stable on small scales. General relativity is recovered at early times and on small scales by this nonlinear interaction via the Vainshtein mechanism. At late time, gravity is strongly modified and the background cosmology shows a phantomlike behavior and the growth rate of structure formation is enhanced. Thus this model leaves distinct signatures in cosmological observations and it can be distinguished from standard LCDM cosmology
An asymptotic relationship between coupling methods for stochastically modeled population processes
This paper is concerned with elucidating a relationship between two common
coupling methods for the continuous time Markov chain models utilized in the
cell biology literature. The couplings considered here are primarily used in a
computational framework by providing reductions in variance for different Monte
Carlo estimators, thereby allowing for significantly more accurate results for
a fixed amount of computational time. Common applications of the couplings
include the estimation of parametric sensitivities via finite difference
methods and the estimation of expectations via multi-level Monte Carlo
algorithms. While a number of coupling strategies have been proposed for the
models considered here, and a number of articles have experimentally compared
the different strategies, to date there has been no mathematical analysis
describing the connections between them. Such analyses are critical in order to
determine the best use for each. In the current paper, we show a connection
between the common reaction path (CRP) method and the split coupling (SC)
method, which is termed coupled finite differences (CFD) in the parametric
sensitivities literature. In particular, we show that the two couplings are
both limits of a third coupling strategy we call the "local-CRP" coupling, with
the split coupling method arising as a key parameter goes to infinity, and the
common reaction path coupling arising as the same parameter goes to zero. The
analysis helps explain why the split coupling method often provides a lower
variance than does the common reaction path method, a fact previously shown
experimentally.Comment: Edited Section 4.
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
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
Inflaton perturbations in brane-world cosmology with induced gravity
We study cosmological perturbations in the brane models with an induced
Einstein-Hilbert term on a brane. We consider an inflaton confined to a de
Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations
excite Kaluza-Klein modes of bulk metric perturbations with mass and where is an
integer. There are two branches ( branches) of solutions for the
background spacetime. In the branch, which includes the self-accelerating
universe, a resonance appears for a mode with due to a spin-0
perturbation with . The self-accelerating universe has a distinct
feature because there is also a helicity-0 mode of spin-2 perturbations with
. In the branch, which can be thought as the Randall-Sundrum
type brane-world with the high energy quantum corrections, there is no
resonance. At high energies, we analytically confirm that four-dimensional
Einstein gravity is recovered, which is related to the disappearance of van
Dam-Veltman-Zakharov discontinuity in de Sitter spacetime.
On sufficiently small scales, we confirm that the lineariaed gravity on the
brane is well described by the Brans-Dicke theory with in
branch and in branch, respectively, which confirms the
existence of the ghost in branch. We also study large scale perturbations.
In branch, the resonance induces a non-trivial anisotropic stress on the
brane via the projection of Weyl tensor in the bulk, but no instability is
shown to exist on the brane.Comment: 20 pages, 4 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
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