100 research outputs found
Gravitational energy and cosmic acceleration
Cosmic acceleration is explained quantitatively, as an apparent effect due to
gravitational energy differences that arise in the decoupling of bound systems
from the global expansion of the universe. "Dark energy" is a misidentification
of those aspects of gravitational energy which by virtue of the equivalence
principle cannot be localised, namely gradients in the energy due to the
expansion of space and spatial curvature variations in an inhomogeneous
universe. A new scheme for cosmological averaging is proposed which solves the
Sandage-de Vaucouleurs paradox. Concordance parameters fit supernovae
luminosity distances, the angular scale of the sound horizon in the CMB
anisotropies, and the effective comoving baryon acoustic oscillation scale seen
in galaxy clustering statistics. Key observational anomalies are potentially
resolved, and unique predictions made, including a quantifiable variance in the
Hubble flow below the scale of apparent homogeneity.Comment: 9 pages, 2 figures. An essay which received Honorable Mention in the
2007 GRF Essay Competition. To appear in a special issue of Int. J. Mod.
Phys.
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
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
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
Quantum-classical transition in Scale Relativity
The theory of scale relativity provides a new insight into the origin of
fundamental laws in physics. Its application to microphysics allows us to
recover quantum mechanics as mechanics on a non-differentiable (fractal)
spacetime. The Schrodinger and Klein-Gordon equations are demonstrated as
geodesic equations in this framework. A development of the intrinsic properties
of this theory, using the mathematical tool of Hamilton's bi-quaternions, leads
us to a derivation of the Dirac equation within the scale-relativity paradigm.
The complex form of the wavefunction in the Schrodinger and Klein-Gordon
equations follows from the non-differentiability of the geometry, since it
involves a breaking of the invariance under the reflection symmetry on the
(proper) time differential element (ds - ds). This mechanism is generalized
for obtaining the bi-quaternionic nature of the Dirac spinor by adding a
further symmetry breaking due to non-differentiability, namely the differential
coordinate reflection symmetry (dx^mu - dx^mu) and by requiring invariance
under parity and time inversion. The Pauli equation is recovered as a
non-relativistic-motion approximation of the Dirac equation.Comment: 28 pages, no figur
Effects of structure formation on the expansion rate of the Universe: An estimate from numerical simulations
General relativistic corrections to the expansion rate of the Universe arise
when the Einstein equations are averaged over a spatial volume in a locally
inhomogeneous cosmology. It has been suggested that they may contribute to the
observed cosmic acceleration. In this paper, we propose a new scheme that
utilizes numerical simulations to make a realistic estimate of the magnitude of
these corrections for general inhomogeneities in (3+1) spacetime. We then
quantitatively calculate the volume averaged expansion rate using N-body
large-scale structure simulations and compare it with the expansion rate in a
standard FRW cosmology. We find that in the weak gravitational field limit, the
converged corrections are slightly larger than the previous claimed 10^{-5}
level, but not large enough nor even of the correct sign to drive the current
cosmic acceleration. Nevertheless, the question of whether the cumulative
effect can significantly change the expansion history of the Universe needs to
be further investigated with strong-field relativity.Comment: 13 pages, 6 figures, improved version published in Phys. Rev.
Phenomenological constraints on Lemaitre-Tolman-Bondi cosmological inhomogeneities from solar system dynamics
We, first, analytically work out the long-term, i.e. averaged over one
orbital revolution, perturbations on the orbit of a test particle moving in a
local Fermi frame induced therein by the cosmological tidal effects of the
inhomogeneous Lemaitre-Tolman-Bondi (LTB) model. The LTB solution has recently
attracted attention, among other things, as a possible explanation of the
observed cosmic acceleration without resorting to dark energy. Then, we
phenomenologically constrain both the parameters K_1 = -\ddot R/R and K_2 =
-\ddot R^'/R^' of the LTB metric in the Fermi frame by using different kinds of
solar system data. The corrections to the standard
Newtonian/Einsteinian precessions of the perihelia of the inner planets
recently estimated with the EPM ephemerides, compared to our predictions for
them, yield K_1 = (4+8) 10^-26 s^-2, K_2 = (3+7) 10^-23 s^-2. The residuals of
the Cassini-based Earth-Saturn range, compared with the numerically integrated
LTB range signature, allow to obtain K_1/2 = 10^-27 s^-2. The LTB-induced
distortions of the orbit of a typical object of the Oort cloud with respect to
the commonly accepted Newtonian picture, based on the observations of the comet
showers from that remote region of the solar system, point towards K_1/2 <=
10^-30-10^-32 s^-2. Such figures have to be compared with those inferred from
cosmological data which are of the order of K1 \approx K2 = -4 10^-36 s^-2.Comment: LaTex2e, 18 pages, 3 tables, 3 figures. Minor changes. Reference
added. Accepted by Journal of Cosmology and Astroparticle Physics (JCAP
Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions
We present new exact solutions {which presumably describe} black holes in the
background of a spatially flat, pressureless dark matter (DM)-, or dark matter
plus dark energy (DM+DE)-, or quintom-dominated universe. These solutions
generalize Lemaitre-Tolman-Bondi metrics. For a DM- or (DM+DE)-dominated
universe, the area of the black hole apparent horizon (AH) decreases with the
expansion of the universe while that of the cosmic AH increases. However, for a
quintom-dominated universe, the black hole AH first shrinks and then expands,
while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated
universe containing a black hole will evolve to the Schwarzschild-de Sitter
solution with both AHs approaching constant size. In a quintom-dominated
universe, the black hole and cosmic AHs will coincide at a certain time, after
which the singularity becomes naked, violating Cosmic Censorship.Comment: 13 pages, 4 figure
How close can an Inhomogeneous Universe mimic the Concordance Model?
Recently, spatially inhomogeneous cosmological models have been proposed as
an alternative to the LCDM model, with the aim of reproducing the late time
dynamics of the Universe without introducing a cosmological constant or dark
energy. This paper investigates the possibility of distinguishing such models
from the standard LCDM using background or large scale structure data. It also
illustrates and emphasizes the necessity of testing the Copernican principle in
order to confront the tests of general relativity with the large scale
structure.Comment: 15 pages, 7 figure
Covariant coarse-graining of inhomogeneous dust flow in General Relativity
A new definition of coarse-grained quantities describing the dust flow in
General Relativity is proposed. It assigns the coarse--grained expansion, shear
and vorticity to finite-size comoving domains of fluid in a covariant,
coordinate-independent manner. The coarse--grained quantities are all
quasi-local functionals, depending only on the geometry of the boundary of the
considered domain. They can be thought of as relativistic generalizations of
simple volume averages of local quantities in a flat space. The procedure is
based on the isometric embedding theorem for S^2 surfaces and thus requires the
boundary of the domain in question to have spherical topology and positive
scalar curvature. We prove that in the limit of infinitesimally small volume
the proposed quantities reproduce the local expansion, shear and vorticity. In
case of irrotational flow we derive the time evolution for the coarse-grained
quantities and show that its structure is very similar to the evolution
equation for their local counterparts. Additional terms appearing in it may
serve as a measure of the backreacton of small-scale inhomogeneities of the
flow on the large-scale motion of the fluid inside the domain and therefore the
result may be interesting in the context of the cosmological backreaction
problem. We also consider the application of the proposed coarse-graining
procedure to a number of known exact solutions of Einstein equations with dust
and show that it yields reasonable results.Comment: 17 pages, 5 figures. Version accepted in Classical and Quantum
Gravity
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