174 research outputs found
Direct reconstruction of dark energy
An important issue in cosmology is reconstructing the effective dark energy
equation of state directly from observations. With so few physically motivated
models, future dark energy studies cannot only be based on constraining a dark
energy parameter space. We present a new non-parametric method which can
accurately reconstruct a wide variety of dark energy behaviour with no prior
assumptions about it. It is simple, quick and relatively accurate, and involves
no expensive explorations of parameter space. The technique uses principal
component analysis and a combination of information criteria to identify real
features in the data, and tailors the fitting functions to pick up trends and
smooth over noise. We find that we can constrain a large variety of w(z) models
to within 10-20 % at redshifts z<1 using just SNAP-quality data.Comment: 5 pages, 4 figures. v2 has added refs plus minor changes. To appear
in PR
Non-Abelian gauge field theory in scale relativity
Gauge field theory is developed in the framework of scale relativity. In this
theory, space-time is described as a non-differentiable continuum, which
implies it is fractal, i.e., explicitly dependent on internal scale variables.
Owing to the principle of relativity that has been extended to scales, these
scale variables can themselves become functions of the space-time coordinates.
Therefore, a coupling is expected between displacements in the fractal
space-time and the transformations of these scale variables. In previous works,
an Abelian gauge theory (electromagnetism) has been derived as a consequence of
this coupling for global dilations and/or contractions. We consider here more
general transformations of the scale variables by taking into account separate
dilations for each of them, which yield non-Abelian gauge theories. We identify
these transformations with the usual gauge transformations. The gauge fields
naturally appear as a new geometric contribution to the total variation of the
action involving these scale variables, while the gauge charges emerge as the
generators of the scale transformation group. A generalized action is
identified with the scale-relativistic invariant. The gauge charges are the
conservative quantities, conjugates of the scale variables through the action,
which find their origin in the symmetries of the ``scale-space''. We thus found
in a geometric way and recover the expression for the covariant derivative of
gauge theory. Adding the requirement that under the scale transformations the
fermion multiplets and the boson fields transform such that the derived
Lagrangian remains invariant, we obtain gauge theories as a consequence of
scale symmetries issued from a geometric space-time description.Comment: 24 pages, LaTe
Average observational quantities in the timescape cosmology
We examine the properties of a recently proposed observationally viable
alternative to homogeneous cosmology with smooth dark energy, the timescape
cosmology. In the timescape model cosmic acceleration is realized as an
apparent effect related to the calibration of clocks and rods of observers in
bound systems relative to volume-average observers in an inhomogeneous geometry
in ordinary general relativity. The model is based on an exact solution to a
Buchert average of the Einstein equations with backreaction. The present paper
examines a number of observational tests which will enable the timescape model
to be distinguished from homogeneous cosmologies with a cosmological constant
or other smooth dark energy, in current and future generations of dark energy
experiments. Predictions are presented for: comoving distance measures; H(z);
the equivalent of the dark energy equation of state, w(z); the Om(z) measure of
Sahni, Shafieloo and Starobinsky; the Alcock-Paczynski test; the baryon
acoustic oscillation measure, D_v; the inhomogeneity test of Clarkson, Bassett
and Lu; and the time drift of cosmological redshifts. Where possible, the
predictions are compared to recent independent studies of similar measures in
homogeneous cosmologies with dark energy. Three separate tests with indications
of results in possible tension with the Lambda CDM model are found to be
consistent with the expectations of the timescape cosmology.Comment: 22 pages, 12 figures; v2 discussion, references added, matches
published versio
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
On cosmological observables in a swiss-cheese universe
Photon geodesics are calculated in a swiss-cheese model, where the cheese is
made of the usual Friedmann-Robertson-Walker solution and the holes are
constructed from a Lemaitre-Tolman-Bondi solution of Einstein's equations. The
observables on which we focus are the changes in the redshift, in the
angular-diameter--distance relation, in the luminosity-distance--redshift
relation, and in the corresponding distance modulus. We find that redshift
effects are suppressed when the hole is small because of a compensation effect
acting on the scale of half a hole resulting from the special case of spherical
symmetry. However, we find interesting effects in the calculation of the
angular distance: strong evolution of the inhomogeneities (as in the approach
to caustic formation) causes the photon path to deviate from that of the FRW
case. Therefore, the inhomogeneities are able to partly mimic the effects of a
dark-energy component. Our results also suggest that the nonlinear effects of
caustic formation in cold dark matter models may lead to interesting effects on
photon trajectories.Comment: 25 pages, 21 figures; replaced to fit the version accepted for
publication in Phys. Rev.
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
Light-cone averages in a swiss-cheese universe
We analyze a toy swiss-cheese cosmological model to study the averaging
problem. In our model, the cheese is the EdS model and the holes are
constructed from a LTB solution. We study the propagation of photons in the
swiss-cheese model, and find a phenomenological homogeneous model to describe
observables. Following a fitting procedure based on light-cone averages, we
find that the the expansion scalar is unaffected by the inhomogeneities. This
is because of spherical symmetry. However, the light-cone average of the
density as a function of redshift is affected by inhomogeneities. The effect
arises because, as the universe evolves, a photon spends more and more time in
the (large) voids than in the (thin) high-density structures. The
phenomenological homogeneous model describing the light-cone average of the
density is similar to the concordance model. Although the sole source in the
swiss-cheese model is matter, the phenomenological homogeneous model behaves as
if it has a dark-energy component. Finally, we study how the equation of state
of the phenomenological model depends on the size of the inhomogeneities, and
find that the equation-of-state parameters w_0 and w_a follow a power-law
dependence with a scaling exponent equal to unity. That is, the equation of
state depends linearly on the distance the photon travels through voids. We
conclude that within our toy model, the holes must have a present size of about
250 Mpc to be able to mimic the concordance model.Comment: 20 pages, 14 figures; replaced to fit the version accepted for
publication in Phys. Rev.
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
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