269 research outputs found
Wave function of the Universe in the early stage of its evolution
In quantum cosmological models, constructed in the framework of
Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its
further expansion is described as a tunneling transition through an effective
barrier between regions with small and large values of the scale factor at
non-zero (or zero) energy. The approach for describing this tunneling consists
of constructing a wave function satisfying an appropriate boundary condition.
There are various ways for defining the boundary condition that lead to
different estimates of the barrier penetrability and the tunneling time.
In order to describe the escape from the tunneling region as accurately as
possible and to construct the total wave function on the basis of its two
partial solutions unambiguously, we use the tunneling boundary condition that
the total wave function must represent only the outgoing wave at the point of
escape from the barrier, where the following definition for the wave is
introduced: the wave is represented by the wave function whose modulus changes
minimally under a variation of the scale factor . We construct a new method
for a direct non-semiclassical calculation of the total stationary wave
function of the Universe, analyze the behavior of this wave function in the
tunneling region, near the escape point and in the asymptotic region, and
estimate the barrier penetrability. We observe oscillations of modulus of wave
function in the external region starting from the turning point which decrease
with increasing of and which are not shown in semiclassical calculations.
The period of such an oscillation decreases uniformly with increasing and
can be used as a fully quantum dynamical characteristic of the expansion of the
Universe.Comment: 19 pages, 21 files for 10 EPS figures, LaTeX svjour style. The Sec.2
(formalism of Wheeler-De Witt equation) is reduced. In Sec.3.1 definition of
the outgoing wave from barrier is defined more accurately. In Sec.4.1
semiclassical calculations of wavew function and penetrability are performed
and comparison with results in fully quantum approach is adde
An Analog Model for Quantum Lightcone Fluctuations in Nonlinear Optics
We propose an analog model for quantum gravity effects using nonlinear
dielectrics. Fluctuations of the spacetime lightcone are expected in quantum
gravity, leading to variations in the flight times of pulses. This effect can
also arise in a nonlinear material. We propose a model in which fluctuations of
a background electric field, such as that produced by a squeezed photon state,
can cause fluctuations in the effective lightcone for probe pulses. This leads
to a variation in flight times analogous to that in quantum gravity. We make
some numerical estimates which suggest that the effect might be large enough to
be observable.Comment: 15 pages, no figure
Wesson's IMT with a Weylian bulk
The foundations of Wesson's induced matter theory are analyzed. It is shown
that the 5D empty bulk must be regarded rather as a Weylian space than as a
Riemannian one.The framework of a Weyl-Dirac version of Wesson's theory is
elaborated and discussed. The bulk possesses in addition to the metric tensor a
Weylian connection vector as well Dirac's gauge function; there are no sources
(mass, current) in the bulk. On the 4D brane one obtains a geometrically based
unified theory of gravitation and electromagnetism with mass, currents and
equations induced by the 5D bulkComment: 29 page
The Hamiltonian of Einstein affine-metric formulation of General Relativity
It is shown that the Hamiltonian of the Einstein affine-metric (first order)
formulation of General Relativity (GR) leads to a constraint structure that
allows the restoration of its unique gauge invariance, four-diffeomorphism,
without the need of any field dependent redefinition of gauge parameters as is
the case for the second order formulation. In the second order formulation of
ADM gravity the need for such a redefinition is the result of the non-canonical
change of variables [arXiv: 0809.0097]. For the first order formulation, the
necessity of such a redefinition "to correspond to diffeomorphism invariance"
(reported by Ghalati [arXiv: 0901.3344]) is just an artifact of using the
Henneaux-Teitelboim-Zanelli ansatz [Nucl. Phys. B 332 (1990) 169], which is
sensitive to the choice of linear combination of tertiary constraints. This
ansatz cannot be used as an algorithm for finding a gauge invariance, which is
a unique property of a physical system, and it should not be affected by
different choices of linear combinations of non-primary first class
constraints. The algorithm of Castellani [Ann. Phys. 143 (1982) 357] is free
from such a deficiency and it leads directly to four-diffeomorphism invariance
for first, as well as for second order Hamiltonian formulations of GR. The
distinct role of primary first class constraints, the effect of considering
different linear combinations of constraints, the canonical transformations of
phase-space variables, and their interplay are discussed in some detail for
Hamiltonians of the second and first order formulations of metric GR. The first
order formulation of Einstein-Cartan theory, which is the classical background
of Loop Quantum Gravity, is also discussed.Comment: 74 page
Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
In spacetimes of dimension greater than four it is natural to consider higher
order (in R) corrections to the Einstein equations. In this letter generalized
Israel junction conditions for a membrane in such a theory are derived. This is
achieved by generalising the Gibbons-Hawking boundary term. The junction
conditions are applied to simple brane world models, and are compared to the
many contradictory results in the literature.Comment: 4 page
Field Theoretical Quantum Effects on the Kerr Geometry
We study quantum aspects of the Einstein gravity with one time-like and one
space-like Killing vector commuting with each other. The theory is formulated
as a \coset nonlinear -model coupled to gravity. The quantum analysis
of the nonlinear -model part, which includes all the dynamical degrees
of freedom, can be carried out in a parallel way to ordinary nonlinear
-models in spite of the existence of an unusual coupling. This means
that we can investigate consistently the quantum properties of the Einstein
gravity, though we are limited to the fluctuations depending only on two
coordinates. We find the forms of the beta functions to all orders up to
numerical coefficients. Finally we consider the quantum effects of the
renormalization on the Kerr black hole as an example. It turns out that the
asymptotically flat region remains intact and stable, while, in a certain
approximation, it is shown that the inner geometry changes considerably however
small the quantum effects may be.Comment: 16 pages, LaTeX. The hep-th number added on the cover, and minor
typos correcte
Brane cosmology with curvature corrections
We study the cosmology of the Randall-Sundrum brane-world where the
Einstein-Hilbert action is modified by curvature correction terms: a
four-dimensional scalar curvature from induced gravity on the brane, and a
five-dimensional Gauss-Bonnet curvature term. The combined effect of these
curvature corrections to the action removes the infinite-density big bang
singularity, although the curvature can still diverge for some parameter
values. A radiation brane undergoes accelerated expansion near the minimal
scale factor, for a range of parameters. This acceleration is driven by the
geometric effects, without an inflaton field or negative pressures. At late
times, conventional cosmology is recovered.Comment: RevTex4, 8 pages, no figures, minor change
Gravitational excitons from extra dimensions
Inhomogeneous multidimensional cosmological models with a higher dimensional
space-time manifold are investigated under dimensional reduction. In the
Einstein conformal frame, small excitations of the scale factors of the
internal spaces near minima of an effective potential have a form of massive
scalar fields in the external space-time. Parameters of models which ensure
minima of the effective potentials are obtained for particular cases and masses
of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20
pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97
The Hamiltonian formulation of General Relativity: myths and reality
A conventional wisdom often perpetuated in the literature states that: (i) a
3+1 decomposition of space-time into space and time is synonymous with the
canonical treatment and this decomposition is essential for any Hamiltonian
formulation of General Relativity (GR); (ii) the canonical treatment
unavoidably breaks the symmetry between space and time in GR and the resulting
algebra of constraints is not the algebra of four-dimensional diffeomorphism;
(iii) according to some authors this algebra allows one to derive only spatial
diffeomorphism or, according to others, a specific field-dependent and
non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac
[Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in
"Gravitation: An Introduction to Current Research" (1962) 227] of the canonical
structure of GR are equivalent. We provide some general reasons why these
statements should be questioned. Points (i-iii) have been shown to be incorrect
in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly
re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that
points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation
of GR. We also demonstrate that ADM and Dirac formulations are related by a
transformation of phase-space variables from the metric to lapse
and shift functions and the three-metric , which is not canonical. This
proves that point (iv) is incorrect. Points (i-iii) are mere consequences of
using a non-canonical change of variables and are not an intrinsic property of
either the Hamilton-Dirac approach to constrained systems or Einstein's theory
itself.Comment: References are added and updated, Introduction is extended,
Subsection 3.5 is added, 83 pages; corresponds to the published versio
Quantum Creation of an Open Inflationary Universe
We discuss a dramatic difference between the description of the quantum
creation of an open universe using the Hartle-Hawking wave function and the
tunneling wave function. Recently Hawking and Turok have found that the
Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is
much smaller that the observed value of Omega > 0.3. Galaxies in such a
universe would be about light years away from each other, so the
universe would be practically structureless. We will argue that the
Hartle-Hawking wave function does not describe the probability of the universe
creation. If one uses the tunneling wave function for the description of
creation of the universe, then in most inflationary models the universe should
have Omega = 1, which agrees with the standard expectation that inflation makes
the universe flat. The same result can be obtained in the theory of a
self-reproducing inflationary universe, independently of the issue of initial
conditions. However, there exist two classes of models where Omega may take any
value, from Omega > 1 to Omega << 1.Comment: 23 pages, 4 figures. New materials are added. In particular, we show
that boundary terms do not help to solve the problem of unacceptably small
Omega in the new model proposed by Hawking and Turok in hep-th/9803156. A
possibility to solve the cosmological constant problem in this model using
the tunneling wave function is discusse
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