157 research outputs found
Timelike and null focusing singularities in spherical symmetry: a solution to the cosmological horizon problem and a challenge to the cosmic censorship hypothesis
Extending the study of spherically symmetric metrics satisfying the dominant
energy condition and exhibiting singularities of power-law type initiated in
SI93, we identify two classes of peculiar interest: focusing timelike
singularity solutions with the stress-energy tensor of a radiative perfect
fluid (equation of state: ) and a set of null singularity
classes verifying identical properties. We consider two important applications
of these results: to cosmology, as regards the possibility of solving the
horizon problem with no need to resort to any inflationary scenario, and to the
Strong Cosmic Censorship Hypothesis to which we propose a class of physically
consistent counter-examples.Comment: 26 pages, 2 figures, LaTeX file. Submitted to Phys. Rev.
Redshift drift in axially symmetric quasi-spherical Szekeres models
Models of inhomogeneous universes constructed with exact solutions of
Einstein's General Relativity have been proposed in the literature with the aim
of reproducing the cosmological data without any need for a dark energy
component. Besides large scale inhomogeneity models spherically symmetric
around the observer, Swiss-cheese models have also been studied. Among them,
Swiss-cheeses where the inhomogeneous patches are modeled by different
particular Szekeres solutions have been used for reproducing the apparent
dimming of the type Ia supernovae (SNIa). However, the problem of fitting such
models to the SNIa data is completely degenerate and we need other constraints
to fully characterize them. One of the tests which is known to be able to
discriminate between different cosmological models is the redshift-drift. This
drift has already been calculated by different authors for
Lema\^itre-Tolman-Bondi (LTB) models. We compute it here for one particular
axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which has
previously been shown to reproduce to a good accuracy the SNIa data, and we
compare the results to the drift in the CDM model and in some LTB
models that can be found in the literature. We show that it is a good
discriminator between them. Then, we discuss our model's remaining degrees of
freedom and propose a recipe to fully constrain them.Comment: 15 pages, 7 figures, minor changes in title, text, figures and
references; conclusions unchanged, this version matches the published versio
The Pauli equation in scale relativity
In standard quantum mechanics, it is not possible to directly extend the
Schrodinger equation to spinors, so the Pauli equation must be derived from the
Dirac equation by taking its non-relativistic limit. Hence, it predicts the
existence of an intrinsic magnetic moment for the electron and gives its
correct value. In the scale relativity framework, the Schrodinger, Klein-Gordon
and Dirac equations have been derived from first principles as geodesics
equations of a non-differentiable and continuous spacetime. Since such a
generalized geometry implies the occurence of new discrete symmetry breakings,
this has led us to write Dirac bi-spinors in the form of bi-quaternions
(complex quaternions). In the present work, we show that, in scale relativity
also, the correct Pauli equation can only be obtained from a non-relativistic
limit of the relativistic geodesics equation (which, after integration, becomes
the Dirac equation) and not from the non-relativistic formalism (that involves
symmetry breakings in a fractal 3-space). The same degeneracy procedure, when
it is applied to the bi-quaternionic 4-velocity used to derive the Dirac
equation, naturally yields a Pauli-type quaternionic 3-velocity. It therefore
corroborates the relevance of the scale relativity approach for the building
from first principles of the quantum postulates and of the quantum tools. This
also reinforces the relativistic and fundamentally quantum nature of spin,
which we attribute in scale relativity to the non-differentiability of the
quantum spacetime geometry (and not only of the quantum space). We conclude by
performing numerical simulations of spinor geodesics, that allow one to gain a
physical geometric picture of the nature of spin.Comment: 22 pages, 2 figures, accepted for publication in J. Phys. A: Math. &
Ge
APSIS - an Artificial Planetary System in Space to probe extra-dimensional gravity and MOND
A proposal is made to test Newton's inverse-square law using the perihelion
shift of test masses (planets) in free fall within a spacecraft located at the
Earth-Sun L2 point. Such an Artificial Planetary System In Space (APSIS) will
operate in a drag-free environment with controlled experimental conditions and
minimal interference from terrestrial sources of contamination. We demonstrate
that such a space experiment can probe the presence of a "hidden" fifth
dimension on the scale of a micron, if the perihelion shift of a "planet" can
be measured to sub-arc-second accuracy. Some suggestions for spacecraft design
are made.Comment: 17 pages, revtex, references added. To appear in Special issue of
IJMP
Generalized quantum potentials in scale relativity
We first recall that the system of fluid mechanics equations (Euler and
continuity) that describes a fluid in irrotational motion subjected to a
generalized quantum potential (in which the constant is no longer reduced to
the standard quantum constant hbar) is equivalent to a generalized Schrodinger
equation. Then we show that, even in the case of the presence of vorticity, it
is also possible to obtain, for a large class of systems, a Schrodinger-like
equation of the vectorial field type from the continuity and Euler equations
including a quantum potential. The same kind of transformation also applies to
a classical charged fluid subjected to an electromagnetic field and to an
additional potential having the form of a quantum potential. Such a fluid can
therefore be described by an equation of the Ginzburg-Landau type, and is
expected to show some superconducting-like properties. Moreover, a Schrodinger
form can be obtained for the fluctuating rotational motion of a solid. In this
case the mass is replaced by the tensor of inertia, and a generalized form of
the quantum potential is derived. We finally reconsider the case of a standard
diffusion process, and we show that, after a change of variable, the diffusion
equation can also be given the form of a continuity and Euler system including
an additional potential energy. Since this potential is exactly the opposite of
a quantum potential, the quantum behavior may be considered, in this context,
as an anti-diffusion.Comment: 33 pages, submitted for publicatio
Tidal Dynamics in Cosmological Spacetimes
We study the relative motion of nearby free test particles in cosmological
spacetimes, such as the FLRW and LTB models. In particular, the influence of
spatial inhomogeneities on local tidal accelerations is investigated. The
implications of our results for the dynamics of the solar system are briefly
discussed. That is, on the basis of the models studied in this paper, we
estimate the tidal influence of the cosmic gravitational field on the orbit of
the Earth around the Sun and show that the corresponding temporal rate of
variation of the astronomical unit is negligibly small.Comment: 12 pages, no figures, REVTeX 4.0; appendix added, new references, and
minor changes throughout; to appear in Classical and Quantum Gravity; v4:
error in (A24) of Appendix A corrected, results and conclusions unchanged. We
thank L. Iorio for pointing out the erro
Model- and calibration-independent test of cosmic acceleration
We present a calibration-independent test of the accelerated expansion of the
universe using supernova type Ia data. The test is also model-independent in
the sense that no assumptions about the content of the universe or about the
parameterization of the deceleration parameter are made and that it does not
assume any dynamical equations of motion. Yet, the test assumes the universe
and the distribution of supernovae to be statistically homogeneous and
isotropic. A significant reduction of systematic effects, as compared to our
previous, calibration-dependent test, is achieved. Accelerated expansion is
detected at significant level (4.3 sigma in the 2007 Gold sample, 7.2 sigma in
the 2008 Union sample) if the universe is spatially flat. This result depends,
however, crucially on supernovae with a redshift smaller than 0.1, for which
the assumption of statistical isotropy and homogeneity is less well
established.Comment: 13 pages, 2 figures, major change
Systematic corrections to the measured cosmological constant as a result of local inhomogeneity
We calculate the systematic inhomogeneity-induced correction to the
cosmological constant that one would infer from an analysis of the luminosities
and redshifts of Type Ia supernovae, assuming a homogeneous universe. The
calculation entails a post-Newtonian expansion within the framework of second
order perturbation theory, wherein we consider the effects of subhorizon
density perturbations in a flat, dust dominated universe. Within this
formalism, we calculate luminosity distances and redshifts along the past light
cone of an observer. The resulting luminosity distance-redshift relation is fit
to that of a homogeneous model in order to deduce the best-fit cosmological
constant density Omega_Lambda. We find that the luminosity distance-redshift
relation is indeed modified, by a small fraction of order 10^{-5}. When fitting
this perturbed relation to that of a homogeneous universe, we find that the
inferred cosmological constant can be surprisingly large, depending on the
range of redshifts sampled. For a sample of supernovae extending from z=0.02
out to z=0.15, we find that Omega_Lambda=0.004. The value of Omega_Lambda has a
large variance, and its magnitude tends to get larger for smaller redshifts,
implying that precision measurements from nearby supernova data will require
taking this effect into account. However, we find that this effect is likely
too small to explain the observed value of Omega_Lambda=0.7. There have been
previous claims of much larger backreaction effects. By contrast to those
calculations, our work is directly related to how observers deduce cosmological
parameters from astronomical data.Comment: 28 pages, 3 figures, revtex4; v2: corrected comments and the section
on previous work; v3: clarified wording. References adde
Local and non-local measures of acceleration in cosmology
Current cosmological observations, when interpreted within the framework of a
homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model,
strongly suggest that the Universe is entering a period of accelerating
expansion. This is often taken to mean that the expansion of space itself is
accelerating. In a general spacetime, however, this is not necessarily true. We
attempt to clarify this point by considering a handful of local and non-local
measures of acceleration in a variety of inhomogeneous cosmological models.
Each of the chosen measures corresponds to a theoretical or observational
procedure that has previously been used to study acceleration in cosmology, and
all measures reduce to the same quantity in the limit of exact spatial
homogeneity and isotropy. In statistically homogeneous and isotropic
spacetimes, we find that the acceleration inferred from observations of the
distance-redshift relation is closely related to the acceleration of the
spatially averaged universe, but does not necessarily bear any resemblance to
the average of the local acceleration of spacetime itself. For inhomogeneous
spacetimes that do not display statistical homogeneity and isotropy, however,
we find little correlation between acceleration inferred from observations and
the acceleration of the averaged spacetime. This shows that observations made
in an inhomogeneous universe can imply acceleration without the existence of
dark energy.Comment: 19 pages, 10 figures. Several references added or amended, some minor
clarifications made in the tex
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