2,155 research outputs found
The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
This study belongs to a series devoted to using Szekeres inhomogeneous models
to develop a theoretical framework where observations can be investigated with
a wider range of possible interpretations. We look here into the growth of
large-scale structure in the models. The Szekeres models are exact solutions to
Einstein's equations that were originally derived with no symmetries. We use a
formulation of the models that is due to Goode and Wainwright, who considered
the models as exact perturbations of an FLRW background. Using the Raychaudhuri
equation, we write for the two classes of the models, exact growth equations in
terms of the under/overdensity and measurable cosmological parameters. The new
equations in the overdensity split into two informative parts. The first part,
while exact, is identical to the growth equation in the usual linearly
perturbed FLRW models, while the second part constitutes exact non-linear
perturbations. We integrate numerically the full exact growth rate equations
for the flat and curved cases. We find that for the matter-dominated era, the
Szekeres growth rate is up to a factor of three to five stronger than the usual
linearly perturbed FLRW cases, reflecting the effect of exact Szekeres
non-linear perturbations. The growth is also stronger than that of the
non-linear spherical collapse model, and the difference between the two
increases with time. This highlights the distinction when we use general
inhomogeneous models where shear and a tidal gravitational field are present
and contribute to the gravitational clustering. Additionally, it is worth
observing that the enhancement of the growth found in the Szekeres models
during the matter-dominated era could suggest a substitute to the argument that
dark matter is needed when using FLRW models to explain the enhanced growth and
resulting large-scale structures that we observe today (abridged)Comment: 18 pages, 4 figures, matches PRD accepted versio
Shear dynamics in Bianchi I cosmologies with R^n-gravity
We give the equations governing the shear evolution in Bianchi spacetimes for
general f(R)-theories of gravity. We consider the case of R^n-gravity and
perform a detailed analysis of the dynamics in Bianchi I cosmologies which
exhibit local rotational symmetry. We find exact solutions and study their
behaviour and stability in terms of the values of the parameter n. In
particular, we found a set of cosmic histories in which the universe is
initially isotropic, then develops shear anisotropies which approaches a
constant value.Comment: 25 pages LaTeX, 6 figures. Revised to match the final version
accepted for publication in CQ
Conformal regularization of Einstein's field equations
To study asymptotic structures, we regularize Einstein's field equations by
means of conformal transformations. The conformal factor is chosen so that it
carries a dimensional scale that captures crucial asymptotic features. By
choosing a conformal orthonormal frame we obtain a coupled system of
differential equations for a set of dimensionless variables, associated with
the conformal dimensionless metric, where the variables describe ratios with
respect to the chosen asymptotic scale structure. As examples, we describe some
explicit choices of conformal factors and coordinates appropriate for the
situation of a timelike congruence approaching a singularity. One choice is
shown to just slightly modify the so-called Hubble-normalized approach, and one
leads to dimensionless first order symmetric hyperbolic equations. We also
discuss differences and similarities with other conformal approaches in the
literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ
Geometry of the quasi-hyperbolic Szekeres models
Geometric properties of the quasi-hyperbolic Szekeres models are discussed
and related to the quasi-spherical Szekeres models. Typical examples of shapes
of various classes of 2-dimensional coordinate surfaces are shown in graphs;
for the hyperbolically symmetric subcase and for the general quasi-hyperbolic
case. An analysis of the mass function is carried out in parallel to an
analogous analysis for the quasi-spherical models. This leads to the conclusion
that determines the density of rest mass averaged over the whole space
of constant time.Comment: 19 pages, 13 figures. This version matches the published tex
Testing expectation theories of decision making without measuring utility or subjective probability
Certain empirical implications of those decision-making theories which involve maximizing an expectation are derived. These implications are all measurement-free, so neither subjective probability nor utility need be measured. Two experiments are reported, the first exploratory and the second intensive and substantial. EV, EU, and SEV theory were inadequate to account for the behavior of 12% or more of the subjects in either experiment. SEU theory was inadequate in 10% or less of the cases in the first experiment and 5% of the cases in the second experiment.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33365/1/0000763.pd
Dynamical systems approach to G2 cosmology
In this paper we present a new approach for studying the dynamics of
spatially inhomogeneous cosmological models with one spatial degree of freedom.
By introducing suitable scale-invariant dependent variables we write the
evolution equations of the Einstein field equations as a system of autonomous
partial differential equations in first-order symmetric hyperbolic format,
whose explicit form depends on the choice of gauge. As a first application, we
show that the asymptotic behaviour near the cosmological initial singularity
can be given a simple geometrical description in terms of the local past
attractor on the boundary of the scale-invariant dynamical state space. The
analysis suggests the name ``asymptotic silence'' to describe the evolution of
the gravitational field near the cosmological initial singularity.Comment: 28 pages, 3 tables, 1 *.eps figure, LaTeX2e (10pt), matches version
accepted for publication by Classical and Quantum Gravit
A fully covariant description of CMB anisotropies
Starting from the exact non-linear description of matter and radiation, a
fully covariant and gauge-invariant formula for the observed temperature
anisotropy of the cosmic microwave background (CBR) radiation, expressed in
terms of the electric () and magnetic () parts of the Weyl
tensor, is obtained by integrating photon geodesics from last scattering to the
point of observation today. This improves and extends earlier work by Russ et
al where a similar formula was obtained by taking first order variations of the
redshift. In the case of scalar (density) perturbations, is related to
the harmonic components of the gravitational potential and the usual
dominant Sachs-Wolfe contribution to the
temperature anisotropy is recovered, together with contributions due to the
time variation of the potential (Rees-Sciama effect), entropy and velocity
perturbations at last scattering and a pressure suppression term important in
low density universes. We also explicitly demonstrate the validity of assuming
that the perturbations are adiabatic at decoupling and show that if the surface
of last scattering is correctly placed and the background universe model is
taken to be a flat dust dominated Friedmann-Robertson-Walker model (FRW), then
the large scale temperature anisotropy can be interpreted as being due to the
motion of the matter relative to the surface of constant temperature which
defines the surface of last scattering on those scales.Comment: 18 pages LaTeX, 1 figure. Submitted to Classical and Quantum Gravity.
Also available at http://shiva.mth.uct.ac.za/preprints/9705.htm
A novel research definition of bladder health in women and girls: Implications for research and public health promotion
BACKGROUND:Bladder health in women and girls is poorly understood, in part, due to absence of a definition for clinical or research purposes. This article describes the process used by a National Institutes of Health funded transdisciplinary research team (The Prevention of Lower Urinary Tract Symptoms [PLUS] Consortium) to develop a definition of bladder health. METHODS:The PLUS Consortium identified currently accepted lower urinary tract symptoms (LUTS) and outlined elements of storage and emptying functions of the bladder. Consistent with the World Health Organization's definition of health, PLUS concluded that absence of LUTS was insufficient and emphasizes the bladder's ability to adapt to short-term physical, psychosocial, and environmental challenges for the final definition. Definitions for subjective experiences and objective measures of bladder dysfunction and health were drafted. An additional bioregulatory function to protect against infection, neoplasia, chemical, or biologic threats was proposed. RESULTS:PLUS proposes that bladder health be defined as: "A complete state of physical, mental, and social well-being related to bladder function and not merely the absence of LUTS. Healthy bladder function permits daily activities, adapts to short-term physical or environmental stressors, and allows optimal well-being (e.g., travel, exercise, social, occupational, or other activities)." Definitions for each element of bladder function are reported with suggested subjective and objective measures. CONCLUSIONS:PLUS used a comprehensive transdisciplinary process to develop a bladder health definition. This will inform instrument development for evaluation of bladder health promotion and prevention of LUTS in research and public health initiatives
Asymptotic silence-breaking singularities
We discuss three complementary aspects of scalar curvature singularities:
asymptotic causal properties, asymptotic Ricci and Weyl curvature, and
asymptotic spatial properties. We divide scalar curvature singularities into
two classes: so-called asymptotically silent singularities and non-generic
singularities that break asymptotic silence. The emphasis in this paper is on
the latter class which have not been previously discussed. We illustrate the
above aspects and concepts by describing the singularities of a number of
representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure
Isotropic singularity in inhomogeneous brane cosmological models
We discuss the asymptotic dynamical evolution of spatially inhomogeneous
brane-world cosmological models close to the initial singularity. By
introducing suitable scale-invariant dependent variables and a suitable gauge,
we write the evolution equations of the spatially inhomogeneous brane
cosmological models with one spatial degree of freedom as a system of
autonomous first-order partial differential equations. We study the system
numerically, and we find that there always exists an initial singularity, which
is characterized by the fact that spatial derivatives are dynamically
negligible. More importantly, from the numerical analysis we conclude that
there is an initial isotropic singularity in all of these spatially
inhomogeneous brane cosmologies for a range of parameter values which include
the physically important cases of radiation and a scalar field source. The
numerical results are supported by a qualitative dynamical analysis and a
calculation of the past asymptotic decay rates. Although the analysis is local
in nature, the numerics indicates that the singularity is isotropic for all
relevant initial conditions. Therefore this analysis, and a preliminary
investigation of general inhomogeneous () models, indicates that it is
plausible that the initial singularity is isotropic in spatially inhomogeneous
brane-world cosmological models and consequently that brane cosmology naturally
gives rise to a set of initial data that provide the conditions for inflation
to subsequently take place.Comment: 32 pages with 8 pictures. submitted to Class. Quant. Gra
- …