64 research outputs found
The Step-Harmonic Potential
We analyze the behavior of a quantum system described by a one-dimensional
asymmetric potential consisting of a step plus a harmonic barrier. We solve the
eigenvalue equation by the integral representation method, which allows us to
classify the independent solutions as equivalence classes of homotopic paths in
the complex plane. We then consider the propagation of a wave packet reflected
by the harmonic barrier and obtain an expression for the interaction time as a
function of the peak energy. For high energies we recover the classical
half-period limit.Comment: 19 pages, 7 figure
Soft singularity crossing and transformation of matter properties
We investigate particular cosmological models, based either on tachyon fields
or on perfect fluids, for which soft future singularities arise in a natural
way. Our main result is the description of a smooth crossing of the soft
singularity in models with an anti-Chaplygin gas or with a particular tachyon
field in the presence of dust. Such a crossing is made possible by certain
transformations of matter properties. Some of these cosmological evolutions
involving tachyons are compatible with SNIa data. We compute numerically their
dynamics involving a first soft singularity crossing, a turning point and a
second soft singulatity crossing during recollapse, ending in a Big Crunch
singularity.Comment: published version, 13 pages, 2 figure panels, new subsection III.D
adde
Will the tachyonic Universe survive the Big Brake?
We investigate a Friedmann universe filled with a tachyon scalar field, which
behaves as dustlike matter in the past, while it is able to accelerate the
expansion rate of the universe at late times. The comparison with type Ia
supernovae (SNIa) data allows for evolutions driving the universe into a Big
Brake. Some of the evolutions leading to a Big Brake exhibit a large variation
of the equation of state parameter at low redshifts which is potentially
observable with future data though hardly detectable with present SNIa data.
The soft Big Brake singularity occurs at finite values of the scale factor,
vanishing energy density and Hubble parameter, but diverging deceleration and
infinite pressure. We show that the geodesics can be continued through the Big
Brake and that our model universe will recollapse eventually in a Big Crunch.
Although the time to the Big Brake strongly depends on the present values of
the tachyonic field and of its time derivative, the time from the Big Brake to
the Big Crunch represents a kind of invariant timescale for all field
parameters allowed by SNIa.Comment: v2: slightly expanded, 14 pages, 5 figures, 3 tables; version to be
published in Phys.Rev.
Equatorial Lensing in the Balasin-Grumiller Galaxy Model
The Balasin-Grumiller model has been the first model employed as an attempt
towards providing a fully general relativistic description of the dynamics of a
disc galaxy. In this paper, we compute the equatorial gravitational lensing
observables of the model. Indeed, our purpose is to investigate the role that
gravitational lensing plays as an observable in distinguishing between the
state-of-the-art galaxy models and the fully general relativistic ones, with
the latter stressing the role of frame-dragging and hence conceivably pointing
to a possible re-weighting of the dark matter content of disc galaxies. We
obtain for the Balasin-Grumiller model the exact formula for the bending angle
of light and we provide a corresponding estimate for the time delay between
images in the equatorial plane. For a reasonable choice for the values of the
parameters of the solution (bulge and scale radiuses, and average rotational
star speeds), the values that we obtain for the bending angle are in agreement
with those observed for typical disc galaxies. On the other hand, the
calculated time delay, which is directly tied to the frame-dragging generated
by the angular momentum of the galaxy, turns out to be some orders of magnitude
larger than the ones measured for the class of galaxies that the
Balasin-Grumiller model would claim to describe. We believe this abnormal
discrepancy to be due to the very nature of the Balasin-Grumiller model.
Namely, it being rigidly rotating, hence providing an unphysical amount of
frame-dragging. Therefore, we conclude that, in spite of its simplicity and its
unquestionable didactical value, the Balasin-Grumiller model is far too crude
to provide an instrument for a reliable general relativistic description of a
disc galaxy and that further work in the fully general relativistic modelling
of galaxies is required to reach a satisfactory stage.Comment: 19 pages and 6 figure
Correspondence between Minkowski and de Sitter Quantum Field Theory
In this letter we show that the ``preferred'' Klein-Gordon Quantum Field
Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a
Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime
satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a
(d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral
condition can be obtained as superposition of d-dimensional de Sitter
Klein-Gordon fields in the preferred vacuum. These results establish a
correspondence between QFT's living on manifolds having different dimensions.
The method exposed here can be applied to study other situations and notably
QFT on Anti de Sitter spacetime.Comment: 7 pages, no figures, typos corrected, added one referenc
Dark matter effects in vacuum spacetime
We analyze a toy model describing an empty spacetime in which the motion of a
test mass (and the trajectories of photons) evidence the presence of a
continuous and homogeneous distribution of matter; however, since the
energy-momentum tensor vanishes, no real matter or energy distribution is
present at all. Thus, a hypothetical observer will conclude that he is immersed
in some sort of dark matter, even though he has no chance to directly detect
it. This suggests yet another possibility of explaining the elusive dark matter
as a purely dynamical effect due to the curvature of spacetime.Comment: 5 pages, 2 figures, expanded with comments about the exact motion and
curvature invariant
Decomposing Quantum Fields on Branes
We provide a method to decompose the two-point function of a quantum field on
a warped manifold in terms of fields living on a lower-dimensional manifold. We
discuss explicit applications to Minkowski, de Sitter and anti-de Sitter
quantum field theories. This decomposition presents a remarkable analogy with
the holography principle, in the sense that physics in d+1 dimensions may be
encoded into the physics in one dimension less. Moreover in a context a la
Randall--Sundrum, the method outlined here allows a mechanism of generation of
mass-spectra in the 3-brane (or more generally a d-1-brane).Comment: 25 page
Can the Chaplygin gas be a plausible model for dark energy?
In this note two cosmological models representing the flat Friedmann Universe
filled with a Chaplygin fluid, with or without dust, are analyzed in terms of
the recently proposed "statefinder" parameters. Trajectories of both models in
the parameter plane are shown to be significantly different w.r.t. "quiessence"
and "tracker" models. The generalized Chaplygin gas model with an equation of
state of the form is also analyzed in terms of the
statefinder parameters.Comment: 6 pages, 2 figure
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