9,517 research outputs found
An analytic model for the transition from decelerated to accelerated cosmic expansion
We consider the scenario where our observable universe is devised as a
dynamical four-dimensional hypersurface embedded in a five-dimensional bulk
spacetime, with a large extra dimension, which is the {\it generalization of
the flat FRW cosmological metric to five dimensions}. This scenario generates a
simple analytical model where different stages of the evolution of the universe
are approximated by distinct parameterizations of the {\it same} spacetime. In
this model the evolution from decelerated to accelerated expansion can be
interpreted as a "first-order" phase transition between two successive stages.
The dominant energy condition allows different parts of the universe to evolve,
from deceleration to acceleration, at different redshifts within a narrow era.
This picture corresponds to the creation of bubbles of new phase, in the middle
of the old one, typical of first-order phase transitions. Taking today, we find that the cross-over from deceleration to acceleration
occurs at , regardless of the equation of state in the very
early universe. In the case of primordial radiation, the model predicts that
the deceleration parameter "jumps" from to at . At the present time and the equation of state of the
universe is , in agreement with observations and some
theoretical predictions.Comment: The abstract and introduction are improved and the discussion section
is expanded. A number of references are adde
Bistability in sine-Gordon: the ideal switch
The sine-Gordon equation, used as the representative nonlinear wave equation,
presents a bistable behavior resulting from nonlinearity and generating
hysteresis properties. We show that the process can be understood in a
comprehensive analytical formulation and that it is a generic property of
nonlinear systems possessing a natural band gap. The approach allows to
discover that sine-Gordon can work as an it ideal switch by reaching a
transmissive regime with vanishing driving amplitude.Comment: Phys. Rev. E, (to be published, May 2005
Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim
In classical Kaluza-Klein theory, with compactified extra dimensions and
without scalar field, the rest mass as well as the electric charge of test
particles are constants of motion. We show that in the case of a large extra
dimension this is no longer so. We propose the Hamilton-Jacobi formalism,
instead of the geodesic equation, for the study of test particles moving in a
five-dimensional background metric. This formalism has a number of advantages:
(i) it provides a clear and invariant definition of rest mass, without the
ambiguities associated with the choice of the parameters used along the motion
in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the
discussion, and (iii) we avoid the difficulties associated with the "splitting"
of the geodesic equation. For particles moving in a general 5D metric, we show
how the effective rest mass, as measured by an observer in 4D, varies as a
consequence of the large extra dimension. Also, the fifth component of the
momentum changes along the motion. This component can be identified with the
electric charge of test particles. With this interpretation, both the rest mass
and the charge vary along the trajectory. The constant of motion is now a
combination of these quantities. We study the cosmological variations of charge
and rest mass in a five-dimensional bulk metric which is used to embed the
standard k = 0 FRW universes. The time variations in the fine structure
"constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2,
references updated. To appear in General Relativity and Gravitatio
Wave-like Solutions for Bianchi type-I cosmologies in 5D
We derive exact solutions to the vacuum Einstein field equations in 5D, under
the assumption that (i) the line element in 5D possesses self-similar symmetry,
in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the
metric tensor is diagonal and independent of the coordinates for ordinary 3D
space. These assumptions lead to three different types of self-similarity in
5D: homothetic, conformal and "wave-like". In this work we present the most
general wave-like solutions to the 5D field equations. Using the standard
technique based on Campbell's theorem, they generate a large number of
anisotropic cosmological models of Bianchi type-I, which can be applied to our
universe after the big-bang, when anisotropies could have played an important
role. We present a complete review of all possible cases of self-similar
anisotropic cosmologies in 5D. Our analysis extends a number of previous
studies on wave-like solutions in 5D with spatial spherical symmetry
Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity
It is well-known that Birkhoff's theorem is no longer valid in theories with
more than four dimensions. Thus, in these theories the effective 4-dimensional
picture allows the existence of different possible, non-Schwarzschild,
scenarios for the description of the spacetime outside of a spherical star,
contrary to general relativity in 4D. We investigate the exterior spacetime of
a spherically symmetric star in the context of Kaluza-Klein gravity. We take a
well-known family of static spherically symmetric solutions of the Einstein
equations in an empty five-dimensional universe, and analyze possible stellar
exteriors that are conformal to the metric induced on four-dimensional
hypersurfaces orthogonal to the extra dimension. All these exteriors are
continuously matched with the interior of the star. Then, without making any
assumptions about the interior solution, we prove the following statement: the
condition that in the weak-field limit we recover the usual Newtonian physics
singles out an unique exterior. This exterior is "similar" to Scharzschild
vacuum in the sense that it has no effect on gravitational interactions.
However, it is more realistic because instead of being absolutely empty, it is
consistent with the existence of quantum zero-point fields. We also examine the
question of how would the deviation from the Schwarzschild vacuum exterior
affect the parameters of a neutron star. In the context of a model star of
uniform density, we show that the general relativity upper limit M/R < 4/9 is
significantly increased as we go away from the Schwarzschild vacuum exterior.
We find that, in principle, the compactness limit of a star can be larger than
1/2, without being a black hole. The generality of our approach is also
discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
Equivalence Between Space-Time-Matter and Brane-World Theories
We study the relationship between space-time-matter (STM) and brane theories.
These two theories look very different at first sight, and have different
motivation for the introduction of a large extra dimension. However, we show
that they are equivalent to each other. First we demonstrate that STM predicts
local and non-local high-energy corrections to general relativity in 4D, which
are identical to those predicted by brane-world models. Secondly, we notice
that in brane models the usual matter in 4D is a consequence of the dependence
of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is
independent of the extra dimension, then the brane is void of matter. Thus, in
brane theory matter and geometry are unified, which is exactly the paradigm
proposed in STM. Consequently, these two 5D theories share the same concepts
and predict the same physics. This is important not only from a theoretical
point of view, but also in practice. We propose to use a combination of both
methods to alleviate the difficult task of finding solutions on the brane. We
show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let
A Note on the Generalized Friedmann Equations for a Thick Brane
Within our thick brane approach previously used to obtain the cosmological
evolution equations on a thick brane embedded in a five-dimensional
Schwarzschild Anti-de Sitter spacetime it is explicitly shown that the
consistency of these equations with the energy conservation equation requires
that, in general, the thickness of the brane evolves in time. This varying
brane thickness entails the possibility that both Newton's gravitational
constant and the effective cosmological constant are time
dependent.Comment: 6 pages,To appear in GR
FLRW Universes from "Wave-Like" Cosmologies in 5D
We consider the evolution of a 4D-universe embedded in a five-dimensional
(bulk) world with a large extra dimension and a cosmological constant. The
cosmology in 5D possesses "wave-like" character in the sense that the metric
coefficients in the bulk are functions of the extra coordinate and time in a
way similar to a pulse or traveling wave propagating along the fifth dimension.
This assumption is motivated by some recent work presenting the big-bang as a
higher dimensional shock wave. We show that this assumption, together with an
equation of state for the effective matter quantities in 4D, allows Einstein's
equations to be fully integrated. We then recover the familiar FLRW universes,
on the four-dimensional hypersurfaces orthogonal to the extra dimension.
Regarding the extra dimension we find that it is {\em growing} in size if the
universe is speeding up its expansion. We also get an estimate for the relative
change of the extra dimension over time. This estimate could have important
observational implications, notably for the time variation of rest mass,
electric charge and the gravitational "constant". Our results extend previous
ones in the literature.Comment: Few comments added, references updated. To appear in Int. J. of Mod.
Phys.
Extra symmetry in the field equations in 5D with spatial spherical symmetry
We point out that the field equations in 5D, with spatial spherical symmetry,
possess an extra symmetry that leaves them invariant. This symmetry corresponds
to certain simultaneous interchange of coordinates and metric coefficients. As
a consequence a single solution in 5D can generate very different scenarios in
4D, ranging from static configurations to cosmological situations. A new
perspective emanates from our work. Namely, that different astrophysical and
cosmological scenarios in 4D might correspond to the same physics in 5D. We
present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
Bistable light detectors with nonlinear waveguide arrays
Bistability induced by nonlinear Kerr effect in arrays of coupled waveguides
is studied and shown to be a means to conceive light detectors that switch
under excitation by a weak signal. The detector is obtained by coupling two
single 1D waveguide to an array of coupled waveguides with adjusted indices and
coupling. The process is understood by analytical description in the
conservative and continuous case and illustrated by numerical simulations of
the model with attenuation.Comment: Phys. Rev. Lett., v.94, (2005, to be published
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