104 research outputs found
Local thermal equilibrium and ideal gas Stephani universes
The Stephani universes that can be interpreted as an ideal gas evolving in
local thermal equilibrium are determined. Five classes of thermodynamic schemes
are admissible, which give rise to five classes of regular models and three
classes of singular models. No Stephani universes exist representing an exact
solution to a classical ideal gas (one for which the internal energy is
proportional to the temperature). But some Stephani universes may approximate a
classical ideal gas at first order in the temperature: all of them are
obtained. Finally, some features about the physical behavior of the models are
pointed out.Comment: 20 page
Inhomogeneous models of interacting dark matter and dark energy
We derive and analyze a class of spherically symmetric cosmological models
whose source is an interactive mixture of inhomogeneous cold dark matter (DM)
and a generic homogeneous dark energy (DE) fluid. If the DE fluid corresponds
to a quintessense scalar field, the interaction term can be associated with a
well motivated non--minimal coupling to the DM component. By constructing a
suitable volume average of the DM component we obtain a Friedman evolution
equation relating this average density with an average Hubble scalar, with the
DE component playing the role of a repulsive and time-dependent term.
Once we select an ``equation of state'' linking the energy density () and
pressure () of the DE fluid, as well as a free function governing the radial
dependence, the models become fully determinate and can be applied to known
specific DE sources, such as quintessense scalar fields or tachyonic fluids.
Considering the simple equation of state with , we show that the free parameters and boundary conditions can be selected
for an adequate description of a local DM overdensity evolving in a suitable
cosmic background that accurately fits current observational data. While a DE
dominated scenario emerges in the asymptotic future, with total and
tending respectively to 1 and -1/2 for all cosmic observers, the effects of
inhomogeneity and anisotropy yield different local behavior and evolution rates
for these parameters in the local overdense region. We suggest that the models
presented can be directly applied to explore the effects of various DE
formalisms on local DM cosmological inhomogeneities.Comment: 15 pages, revtex4, 10 eps figure
Radial asymptotics of Lemaitre-Tolman-Bondi dust models
We examine the radial asymptotic behavior of spherically symmetric
Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along
radial rays, which are spacelike geodesics parametrized by proper length
, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing
quasi-local scalars defined as integral functions along the rays, we obtain a
complete and covariant representation of the models, leading to an initial
value parametrization in which all scalars can be given by scaling laws
depending on two metric scale factors and two basic initial value functions.
Considering regular "open" LTB models whose space slices allow for a diverging
, we provide the conditions on the radial coordinate so that its
asymptotic limit corresponds to the limit as . The "asymptotic
state" is then defined as this limit, together with asymptotic series expansion
around it, evaluated for all metric functions, covariant scalars (local and
quasi-local) and their fluctuations. By looking at different sets of initial
conditions, we examine and classify the asymptotic states of parabolic,
hyperbolic and open elliptic models admitting a symmetry center. We show that
in the radial direction the models can be asymptotic to any one of the
following spacetimes: FLRW dust cosmologies with zero or negative spatial
curvature, sections of Minkowski flat space (including Milne's space), sections
of the Schwarzschild--Kruskal manifold or self--similar dust solutions.Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style.
Typos corrected and an important reference added. Accepted for publication in
General Relativity and Gravitatio
Collapsing Spheres Satisfying An "Euclidean Condition"
We study the general properties of fluid spheres satisfying the heuristic
assumption that their areas and proper radius are equal (the Euclidean
condition). Dissipative and non-dissipative models are considered. In the
latter case, all models are necessarily geodesic and a subclass of the
Lemaitre-Tolman-Bondi solution is obtained. In the dissipative case solutions
are non-geodesic and are characterized by the fact that all non-gravitational
forces acting on any fluid element produces a radial three-acceleration
independent on its inertial mass.Comment: 1o pages, Latex. Title changed and text shortened to fit the version
to appear in Gen.Rel.Grav
An inverse approach to Einstein's equations for non-conducting fluids
We show that a flow (timelike congruence) in any type warped product
spacetime is uniquely and algorithmically determined by the condition of zero
flux. (Though restricted, these spaces include many cases of interest.) The
flow is written out explicitly for canonical representations of the spacetimes.
With the flow determined, we explore an inverse approach to Einstein's
equations where a phenomenological fluid interpretation of a spacetime follows
directly from the metric irrespective of the choice of coordinates. This
approach is pursued for fluids with anisotropic pressure and shear viscosity.
In certain degenerate cases this interpretation is shown to be generically not
unique. The framework developed allows the study of exact solutions in any
frame without transformations. We provide a number of examples, in various
coordinates, including spacetimes with and without unique interpretations. The
results and algorithmic procedure developed are implemented as a computer
algebra program called GRSource.Comment: 9 pages revtex4. Final form to appear in Phys Rev
Effects of inhomogeneities on apparent cosmological observables: "fake" evolving dark energy
Using the exact Lemaitre-Bondi-Tolman solution with a non-vanishing
cosmological constant , we investigate how the presence of a local
spherically-symmetric inhomogeneity can affect apparent cosmological
observables, such as the deceleration parameter or the effective equation of
state of dark energy (DE), derived from the luminosity distance under the
assumption that the real space-time is exactly homogeneous and isotropic. The
presence of a local underdensity is found to produce apparent phantom behavior
of DE, while a locally overdense region leads to apparent quintessence
behavior. We consider relatively small large scale inhomogeneities which today
are not linear and could be seeded by primordial curvature perturbations
compatible with CMB bounds. Our study shows how observations in an
inhomogeneous CDM universe with initial conditions compatible with the
inflationary beginning, if interpreted under the wrong assumption of
homogeneity, can lead to the wrong conclusion about the presence of "fake"
evolving dark energy instead of .Comment: 22 pages, 19 figures,Final version to appear in European Physical
Journal
CDM Accelerating Cosmology as an Alternative to LCDM model
A new accelerating cosmology driven only by baryons plus cold dark matter
(CDM) is proposed in the framework of general relativity. In this model the
present accelerating stage of the Universe is powered by the negative pressure
describing the gravitationally-induced particle production of cold dark matter
particles. This kind of scenario has only one free parameter and the
differential equation governing the evolution of the scale factor is exactly
the same of the CDM model. For a spatially flat Universe, as predicted
by inflation (), it is found that the
effectively observed matter density parameter is ,
where is the constant parameter specifying the CDM particle creation
rate. The supernovae test based on the Union data (2008) requires so that as independently derived from weak
gravitational lensing, the large scale structure and other complementary
observations.Comment: 6 pages, 3 figure
A new ghost cell/level set method for moving boundary problems:application to tumor growth
In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth
Detecting violations of temporal regularities in waking and sleeping two-month-old infants
Correctly processing rapid sequences of sounds is essential for developmental milestones, such as language acquisition. We investigated the sensitivity of two-month-old infants to violations of a temporal regularity, by recording event-related brain potentials (ERP) in an auditory oddball paradigm from 36 waking and 40 sleeping infants. Standard tones were presented at a regular 300 ms inter-stimulus interval (ISI). One deviant, otherwise identical to the standard, was preceded by a 100 ms ISI. Two other deviants, presented with the standard ISI, differed from the standard in their spectral makeup. We found significant differences between ERP responses elicited by the standard and each of the deviant sounds. The results suggest that the ability to extract both temporal and spectral regularities from a sound sequence is already functional within the first few months of life. The scalp distribution of all three deviant-stimulus responses was influenced by the infants‟ state of alertness
Perceiving the equation of state of Dark Energy while living in a Cold Spot
The Cold Spot could be an adiabatic perturbation on the surface of last
scattering, in which case it is an over-density with comoving radius of the
order of 1 Gpc. We assess the effect that living in a similar structure,
without knowing it, has on our perception of the equation of state of Dark
Energy. We find that structures of dimensions such that they could cause the
Cold Spot on the CMB, affect the perceived equation of state of Dark Energy
possibly up to ten percent.Comment: 17 pages, 5 figures, matches published versio
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