45 research outputs found
Braneworld reheating in the bulk inflaton model
In the context of the braneworld inflation driven by a bulk scalar field, we
study the energy dissipation from the bulk scalar field into the matter on the
brane in order to understand the reheating after inflation. Deriving the
late-time behavior of the bulk field with dissipation by using the Green's
function method, we give a rigorous justification of the statement that the
standard reheating process is reproduced in this bulk inflaton model as long as
the Hubble parameter on the brane and the mass of the bulk scalar field are
much smaller than the 5-dimensional inverse curvature scale. Our result
supports the idea that the brane inflation model caused by a bulk scalar field
is expected to be a viable alternative scenario of the early universe.Comment: 5 pages, no figures, 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
(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.
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
Bulk scalar field in the braneworld can mimic the 4D inflaton dynamics
Based on the recently proposed scenario of inflation driven by a bulk scalar
field in the braneworld of the Randall-Sundrum (RS) type, we investigate the
dynamics of a bulk scalar field on the inflating braneworld. We derive the late
time behavior of the bulk scalar field by analyzing the property of the
retarded Green function. We find that the late time behavior is basically
dominated by a single (or a pair of) pole(s) in the Green function irrespective
of the initial condition and of the signature of , where
is the potential of the bulk scalar field. Including the lowest order
back-reaction to the geometry, this late time behavior can be well approximated
by an effective 4-dimensional scalar field with . The
mapping to the 4-dimensional effective theory is given by a simple scaling of
the potential with a redefinition of the field. Our result supports the picture
that the scenario of inflation driven by a bulk scalar field works in a quite
similar way to that in the standard 4-dimensional cosmology.Comment: 12 pages, no figures, final version to be published in PR
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
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.
Vacuum solutions of the gravitational field equations in the brane world model
We consider some classes of solutions of the static, spherically symmetric
gravitational field equations in the vacuum in the brane world scenario, in
which our Universe is a three-brane embedded in a higher dimensional
space-time. The vacuum field equations on the brane are reduced to a system of
two ordinary differential equations, which describe all the geometric
properties of the vacuum as functions of the dark pressure and dark radiation
terms (the projections of the Weyl curvature of the bulk, generating non-local
brane stresses). Several classes of exact solutions of the vacuum gravitational
field equations on the brane are derived. In the particular case of a vanishing
dark pressure the integration of the field equations can be reduced to the
integration of an Abel type equation. A perturbative procedure, based on the
iterative solution of an integral equation, is also developed for this case.
Brane vacuums with particular symmetries are investigated by using Lie group
techniques. In the case of a static vacuum brane admitting a one-parameter
group of conformal motions the exact solution of the field equations can be
found, with the functional form of the dark radiation and pressure terms
uniquely fixed by the symmetry. The requirement of the invariance of the field
equations with respect to the quasi-homologous group of transformations also
imposes a unique, linear proportionality relation between the dark energy and
dark pressure. A homology theorem for the static, spherically symmetric
gravitational field equations in the vacuum on the brane is also proven.Comment: 13 pages, no figures, to appear in PR
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp