71 research outputs found
The mathematical basis for deterministic quantum mechanics
If there exists a classical, i.e. deterministic theory underlying quantum
mechanics, an explanation must be found of the fact that the Hamiltonian, which
is defined to be the operator that generates evolution in time, is bounded from
below. The mechanism that can produce exactly such a constraint is identified
in this paper. It is the fact that not all classical data are registered in the
quantum description. Large sets of values of these data are assumed to be
indistinguishable, forming equivalence classes. It is argued that this should
be attributed to information loss, such as what one might suspect to happen
during the formation and annihilation of virtual black holes.
The nature of the equivalence classes is further elucidated, as it follows
from the positivity of the Hamiltonian. Our world is assumed to consist of a
very large number of subsystems that may be regarded as approximately
independent, or weakly interacting with one another. As long as two (or more)
sectors of our world are treated as being independent, they all must be
demanded to be restricted to positive energy states only. What follows from
these considerations is a unique definition of energy in the quantum system in
terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations
adde
A symmetry for vanishing cosmological constant
Two different realizations of a symmetry principle that impose a zero
cosmological constant in an extra-dimensional set-up are studied. The symmetry
is identified by multiplication of the metric by minus one. In the first
realization of the symmetry this is provided by a symmetry transformation that
multiplies the coordinates by the imaginary number i. In the second realization
this is accomplished by a symmetry transformation that multiplies the metric
tensor by minus one. In both realizations of the symmetry the requirement of
the invariance of the gravitational action under the symmetry selects out the
dimensions given by D = 2(2n+1), n=0,1,2,... and forbids a bulk cosmological
constant. Another attractive aspect of the symmetry is that it seems to be more
promising for quantization when compared to the usual scale symmetry. The
second realization of the symmetry is more attractive in that it is posible to
make a possible brane cosmological constant zero in a simple way by using the
same symmetry, and the symmetry may be identified by reflection symmetry in
extra dimensions.Comment: Talk in the conference IRGAC 2006, 2nd International Conference on
Quantum Theories and Renormalization Group in Gravity and Cosmology,
Barcelon
Complex Lagrangians and phantom cosmology
Motivated by the generalization of quantum theory for the case of
non-Hermitian Hamiltonians with PT symmetry, we show how a classical
cosmological model describes a smooth transition from ordinary dark energy to
the phantom one. The model is based on a classical complex Lagrangian of a
scalar field. Specific symmetry properties analogous to PT in non-Hermitian
quantum mechanics lead to purely real equation of motion.Comment: 11 pages, to be published in J.Phys.A, refs. adde
Brane Induced Gravity, its Ghost and the Cosmological Constant Problem
"Brane Induced Gravity" is regarded as a promising framework for addressing
the cosmological constant problem, but it also suffers from a ghost instability
for parameter values that make it phenomenologically viable. We carry out a
detailed analysis of codimension > 2 models employing gauge invariant variables
in a flat background approximation. It is argued that using instead a curved
background sourced by the brane would not resolve the ghost issue, unless a
very specific condition is satisfied (if satisfiable at all). As for other
properties of the model, from an explicit analysis of the 4-dimensional
graviton propagator we extract a mass, a decay width and a momentum dependent
modification of the gravitational coupling for the spin 2 mode. In the flat
space approximation, the mass of the problematic spin 0 ghost is instrumental
in filtering out a brane cosmological constant. The mass replaces a background
curvature that would have had the same function. The optical theorem is used to
demonstrate the suppression of graviton leakage into the uncompactified bulk.
Then, we derive the 4-dimensional effective action for gravity and show that
general covariance is spontaneously broken by the bulk-brane setup. This
provides a natural realization of the gravitational Higgs mechanism. We also
show that the addition of extrinsic curvature dependent terms has no bearing on
linearized brane gravity.Comment: v2: LaTeX, JHEP style, 41 pages, 3 eps figures. Partly rewritten to
improve presentation, results unchanged, published versio
Late transient acceleration of the universe in string theory on
Recently, in Gong {\em et al} \cite{GWW07} and Wang and Santos \cite{WS07} it
was shown that the effective cosmological constant on each of the two orbifold
branes can be easily lowered to its current observational value, by using the
large extra dimensions in the framework of both M-Theory and string theory on
. In this paper, we study the current acceleration of the
universe, using the formulas developed in \cite{WS07}. We first construct
explicitly time-dependent solution to the 10-dimensional bulk of the
Neveu-Schwarz/Neveu-Schwarz sector, compactified on a 5-dimensional torus.
Then, we write down the generalized Friedmann equations on each of the two
dynamical branes, and fit the models to the 182 gold supernova Ia data and the
BAO parameter from SDSS, using both of our MINUIT and Monte-Carlo Markov Chain
(MCMC) codes. With the best fitting values of the parameters involved as
initial conditions, we integrate the generalized Friedmann equations
numerically and find the future evolution of the universe. We find that it
depends on the choice of the radion potentials of the
branes. In particular, when choosing them to be the Goldberger-Wise potentials,
, we find that
the current acceleration of the universe driven by the effective cosmological
constant is only temporary. Due to the effects of the potentials, the universe
will be finally in its decelerating expansion phase again. We also study the
proper distance between the two branes, and find that it remains almost
constant during the whole future evolution of the universe in all the models
considered.Comment: revtex4, 18 figures. Typos corrected and new References added.
Version to be published in JCA
Nonsaturated Holographic Dark Energy
It has been well established by today that the concept of holographic dark
energy (HDE) does entail a serious candidate for the dark energy of the
universe. Here we deal with models where the holographic bound for dark energy
is not saturated for a large portion of the history of the universe. This is
particularly compelling when the IR cutoff is set by the Hubble scale, since
otherwise a transition from a decelerated to an accelerated era cannot be
obtained for a spatially flat universe. We demonstrate by three generic but
disparate dynamical models, two of them containing a variable Newton constant,
that transition between the two eras is always obtained for the IR cutoff in
the form of the Hubble scale and the nonsaturated HDE. We also give arguments
of why such a choice for the dark energy is more consistent and favored over
the widely accepted saturated form.Comment: 9 pages, minor revision, to appear in JCA
Vacuum properties of nonsymmetric gravity in de Sitter space
We consider quantum effects of a massive antisymmetric tensor field on the
dynamics of de Sitter space-time. Our starting point is the most general,
stable, linearized Lagrangian arising in nonsymmetric gravitational theories
(NGTs), where part of the antisymmetric field mass is generated by the
cosmological term. We construct a renormalization group (RG) improved effective
action by integrating out one loop vacuum fluctuations of the antisymmetric
tensor field and show that, in the limit when the RG scale goes to zero, the
Hubble parameter -- and thus the effective cosmological constant -- relaxes
rapidly to zero. We thus conclude that quantum loop effects in de Sitter space
can dramatically change the infrared sector of the on-shell gravity, making the
expansion rate insensitive to the original (bare) cosmological constant.Comment: 32 pages, 2 eps figure
MSLED, Neutrino Oscillations and the Cosmological Constant
We explore the implications for neutrino masses and mixings within the
minimal version of the supersymmetric large-extra-dimensions scenario (MSLED).
This model was proposed in {\tt hep-ph/0404135} to extract the phenomenological
implications of the promising recent attempt (in {\tt hep-th/0304256}) to
address the cosmological constant problem. Remarkably, we find that the
simplest couplings between brane and bulk fermions within this approach can
lead to a phenomenologically-viable pattern of neutrino masses and mixings that
is also consistent with the supernova bounds which are usually the bane of
extra-dimensional neutrino models. Under certain circumstances the MSLED
scenario can lead to a lepton mixing (PMNS) matrix close to the so-called
bi-maximal or the tri-bimaximal forms (which are known to provide a good
description of the neutrino oscillation data). We discuss the implications of
MSLED models for neutrino phenomenology.Comment: 38 pages, 1 figure; Reposted with a few additional reference
Cosmic coincidences and relic neutrinos
A simple phenomenological description for the energy transfer between a
variable cosmological constant (CC) and a gas of relic neutrinos in an
expanding universe can account for a near coincidence between the neutrino and
dark-energy densities to hold over a significant portion of the history of the
universe. Although such a cosmological setup may promote neutrinos to
mass-varying particles, both with slow and quick neutrino mass changing with
the expansion of the universe naturally implemented in the model, it also works
equally well for static neutrino masses. We also stress what sort of models for
variable CC can potentially underpin the above scenario.Comment: 7 pages, LaTeX, based on the on the talk at IRGAC-2006 (Barcelona,
July 11-15, 2006), accepted for publication in Journal of Physics
Is the evidence for dark energy secure?
Several kinds of astronomical observations, interpreted in the framework of
the standard Friedmann-Robertson-Walker cosmology, have indicated that our
universe is dominated by a Cosmological Constant. The dimming of distant Type
Ia supernovae suggests that the expansion rate is accelerating, as if driven by
vacuum energy, and this has been indirectly substantiated through studies of
angular anisotropies in the cosmic microwave background (CMB) and of spatial
correlations in the large-scale structure (LSS) of galaxies. However there is
no compelling direct evidence yet for (the dynamical effects of) dark energy.
The precision CMB data can be equally well fitted without dark energy if the
spectrum of primordial density fluctuations is not quite scale-free and if the
Hubble constant is lower globally than its locally measured value. The LSS data
can also be satisfactorily fitted if there is a small component of hot dark
matter, as would be provided by neutrinos of mass 0.5 eV. Although such an
Einstein-de Sitter model cannot explain the SNe Ia Hubble diagram or the
position of the `baryon acoustic oscillation' peak in the autocorrelation
function of galaxies, it may be possible to do so e.g. in an inhomogeneous
Lemaitre-Tolman-Bondi cosmology where we are located in a void which is
expanding faster than the average. Such alternatives may seem contrived but
this must be weighed against our lack of any fundamental understanding of the
inferred tiny energy scale of the dark energy. It may well be an artifact of an
oversimplified cosmological model, rather than having physical reality.Comment: 12 pages, 5 figures; to appear in a special issue of General
Relativity and Gravitation, eds. G.F.R. Ellis et al; Changes: references
reformatted in journal style - text unchange
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