145 research outputs found
Backreaction in Late-Time Cosmology
We review the effect of the formation of nonlinear structures on the expansion rate, spatial curvature, and light propagation in the universe, focusing on the possibility that this effect could explain cosmological observations without requiring the introduction of dark energy or modified gravity. We concentrate on explaining the relevant physics and highlighting open questions.Peer reviewe
Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
The ``Newtonian'' theory of spatially unbounded, self--gravitating,
pressureless continua in Lagrangian form is reconsidered. Following a review of
the pertinent kinematics, we present alternative formulations of the Lagrangian
evolution equations and establish conditions for the equivalence of the
Lagrangian and Eulerian representations. We then distinguish open models based
on Euclidean space from closed models based (without loss of generality)
on a flat torus \T^3. Using a simple averaging method we show that the
spatially averaged variables of an inhomogeneous toroidal model form a
spatially homogeneous ``background'' model and that the averages of open
models, if they exist at all, in general do not obey the dynamical laws of
homogeneous models. We then specialize to those inhomogeneous toroidal models
whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution
equations which govern the (conformally rescaled) displacement of the
inhomogeneous flow with respect to its homogeneous background. Finally, we set
up an iteration scheme and prove that the resulting equations have unique
solutions at any order for given initial data, while for open models there
exist infinitely many different solutions for given data.Comment: submitted to G.R.G., TeX 30 pages; AEI preprint 01
Dark Energy from structure: a status report
The effective evolution of an inhomogeneous universe model in any theory of
gravitation may be described in terms of spatially averaged variables. In
Einstein's theory, restricting attention to scalar variables, this evolution
can be modeled by solutions of a set of Friedmann equations for an effective
volume scale factor, with matter and backreaction source terms. The latter can
be represented by an effective scalar field (`morphon field') modeling Dark
Energy.
The present work provides an overview over the Dark Energy debate in
connection with the impact of inhomogeneities, and formulates strategies for a
comprehensive quantitative evaluation of backreaction effects both in
theoretical and observational cosmology. We recall the basic steps of a
description of backreaction effects in relativistic cosmology that lead to
refurnishing the standard cosmological equations, but also lay down a number of
challenges and unresolved issues in connection with their observational
interpretation.
The present status of this subject is intermediate: we have a good
qualitative understanding of backreaction effects pointing to a global
instability of the standard model of cosmology; exact solutions and
perturbative results modeling this instability lie in the right sector to
explain Dark Energy from inhomogeneities. It is fair to say that, even if
backreaction effects turn out to be less important than anticipated by some
researchers, the concordance high-precision cosmology, the architecture of
current N-body simulations, as well as standard perturbative approaches may all
fall short in correctly describing the Late Universe.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy, 59
pages, 2 figures; matches published versio
Correspondence between kinematical backreaction and scalar field cosmologies - the `morphon field'
Spatially averaged inhomogeneous cosmologies in classical general relativity
can be written in the form of effective Friedmann equations with sources that
include backreaction terms. In this paper we propose to describe these
backreaction terms with the help of a homogeneous scalar field evolving in a
potential; we call it the `morphon field'. This new field links classical
inhomogeneous cosmologies to scalar field cosmologies, allowing to reinterpret,
e.g., quintessence scenarios by routing the physical origin of the scalar field
source to inhomogeneities in the Universe. We investigate a one-parameter
family of scaling solutions to the backreaction problem. Subcases of these
solutions (all without an assumed cosmological constant) include
scale-dependent models with Friedmannian kinematics that can mimic the presence
of a cosmological constant or a time-dependent cosmological term. We explicitly
reconstruct the scalar field potential for the scaling solutions, and discuss
those cases that provide a solution to the Dark Energy and coincidence
problems. In this approach, Dark Energy emerges from morphon fields, a
mechanism that can be understood through the proposed correspondence: the
averaged cosmology is characterized by a weak decay (quintessence) or growth
(phantom quintessence) of kinematical fluctuations, fed by `curvature energy'
that is stored in the averaged 3-Ricci curvature. We find that the late-time
trajectories of those models approach attractors that lie in the future of a
state that is predicted by observational constraints.Comment: 36 pages and 6 Figures, matches published version in Class.Quant.Gra
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.
MR Imaging of Prostate Cancer: Diffusion Weighted Imaging and (3D) Hydrogen 1 (1H) MR Spectroscopy in Comparison with Histology
Purpose. To evaluate retrospectively the impact of diffusion weighted imaging (DWI) and (3D) hydrogen 1 (1H) MR-spectroscopy (MRS) on the detection of prostatic cancer in comparison to histological examinations. Materials and Methods: 50 patients with suspicion of prostate cancer underwent a MRI examination at a 1.5T scanner. The prostate was divided into sextants. Regions of interest were placed in each sextant to evaluate the apparent diffusion coefficient (ADC)-values. The results of the DWI as well as MRS were compared retrospectively with the findings of the histological examination. Sensitivity and specificity of ADC and metabolic ratio (MET)—both separately and in combination—for identification of tumor tissue was computed for variable discrimination thresholds to evaluate its receiver operator characteristic (ROC). An association between ADC, MET and Gleason score was tested by the non-parametric Spearman ρ-test. Results. The average ADC-value was 1.65 ± 0.32mm2/s × 10−3 in normal tissue and 0.96±0.24 mm2/s × 10−3 in tumor tissue (mean ± 1 SD). MET was 0.418 ± 0.431 in normal tissue and 2.010 ± 1.649 in tumor tissue. The area under the ROC curve was 0.966 (95%-confidence interval 0.941–0.991) and 0.943 (0.918–0.968) for DWI and MRS, respectively. There was a highly significant negative correlation between ADC-value and the Gleason score in the tumor-positive tissue probes (n = 62, ρ = −0.405, P = .001). MRS did not show a significant correlation with the Gleason score (ρ = 0.117, P = .366). By using both the DWI and MRS, the regression model provided sensitivity and specificity for detection of tumor of 91.9% and 98.3%, respectively. Conclusion. The results of our study showed that both DWI and MRS should be considered as an additional and complementary tool to the T2-weighted MRI for detecting prostate cancer
Can the Acceleration of Our Universe Be Explained by the Effects of Inhomogeneities?
No. It is simply not plausible that cosmic acceleration could arise within
the context of general relativity from a back-reaction effect of
inhomogeneities in our universe, without the presence of a cosmological
constant or ``dark energy.'' We point out that our universe appears to be
described very accurately on all scales by a Newtonianly perturbed FLRW metric.
(This assertion is entirely consistent with the fact that we commonly encounter
.) If the universe is accurately described by a
Newtonianly perturbed FLRW metric, then the back-reaction of inhomogeneities on
the dynamics of the universe is negligible. If not, then it is the burden of an
alternative model to account for the observed properties of our universe. We
emphasize with concrete examples that it is {\it not} adequate to attempt to
justify a model by merely showing that some spatially averaged quantities
behave the same way as in FLRW models with acceleration. A quantity
representing the ``scale factor'' may ``accelerate'' without there being any
physically observable consequences of this acceleration. It also is {\it not}
adequate to calculate the second-order stress energy tensor and show that it
has a form similar to that of a cosmological constant of the appropriate
magnitude. The second-order stress energy tensor is gauge dependent, and if it
were large, contributions of higher perturbative order could not be neglected.
We attempt to clear up the apparent confusion between the second-order stress
energy tensor arising in perturbation theory and the ``effective stress energy
tensor'' arising in the ``shortwave approximation.''Comment: 20 pages, 1 figure, several footnotes and references added, version
accepted for publication in CQG;some clarifying comments adde
Spherically Symmetric Solutions in Macroscopic Gravity
Schwarzschild's solution to the Einstein Field Equations was one of the first
and most important solutions that lead to the understanding and important
experimental tests of Einstein's theory of General Relativity. However,
Schwarzschild's solution is essentially based on an ideal theory of
gravitation, where all inhomogeneities are ignored. Therefore, any
generalization of the Schwarzschild solution should take into account the
effects of small perturbations that may be present in the gravitational field.
The theory of Macroscopic Gravity characterizes the effects of the
inhomogeneities through a non-perturbative and covariant averaging procedure.
With similar assumptions on the geometry and matter content, a solution to the
averaged field equations as dictated by Macroscopic Gravity are derived. The
resulting solution provides a possible explanation for the flattening of
galactic rotation curves, illustrating that Dark Matter is not real but may
only be the result of averaging inhomogeneities in a spherically symmetric
background.Comment: 14 pages, added and updated references, some paragraphs rewritten for
clarity, typographical errors fixed, results have not change
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