899 research outputs found
Information Entropy in Cosmology
The effective evolution of an inhomogeneous cosmological model may be
described in terms of spatially averaged variables. We point out that in this
context, quite naturally, a measure arises which is identical to a fluid model
of the `Kullback-Leibler Relative Information Entropy', expressing the
distinguishability of the local inhomogeneous mass density field from its
spatial average on arbitrary compact domains. We discuss the time-evolution of
`effective information' and explore some implications. We conjecture that the
information content of the Universe -- measured by Relative Information Entropy
of a cosmological model containing dust matter -- is increasing.Comment: LateX, PRLstyle, 4 pages; to appear in PR
Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust
In standard perturbation approaches and N-body simulations, inhomogeneities
are described to evolve on a predefined background cosmology, commonly taken as
the homogeneous-isotropic solutions of Einstein's field equations
(Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make
physical sense, this background cosmology must provide a reasonable description
of the effective, i.e. spatially averaged, evolution of structure
inhomogeneities also in the nonlinear regime. Guided by the insights that (i)
the average over an inhomogeneous distribution of matter and geometry is in
general not given by a homogeneous solution of general relativity, and that
(ii) the class of FLRW cosmologies is not only locally but also globally
gravitationally unstable in relevant cases, we here develop a perturbation
approach that describes the evolution of inhomogeneities on a general
background being defined by the spatially averaged evolution equations. This
physical background interacts with the formation of structures. We derive and
discuss the resulting perturbation scheme for the matter model `irrotational
dust' in the Lagrangian picture, restricting our attention to scalar
perturbations.Comment: 18 pages. Matches published version in CQ
Averaging procedure in variable-G cosmologies
Previous work in the literature had built a formalism for spatially averaged
equations for the scale factor, giving rise to an averaged Raychaudhuri
equation and averaged Hamiltonian constraint, which involve a backreaction
source term. The present paper extends these equations to include models with
variable Newton parameter and variable cosmological term, motivated by the
nonperturbative renormalization program for quantum gravity based upon the
Einstein-Hilbert action. We focus on the Brans-Dicke form of the
renormalization-group improved action functional. The coupling between
backreaction and spatially averaged three-dimensional scalar curvature is found
to survive, and a variable-G cosmic quintet is found to emerge. Interestingly,
under suitable assumptions, an approximate solution can be found where the
early universe tends to a FLRW model, while keeping track of the original
inhomogeneities through three effective fluids. The resulting qualitative
picture is that of a universe consisting of baryons only, while inhomogeneities
average out to give rise to the full dark-side phenomenology.Comment: 20 pages. In the new version, all original calculations have been
improved, and the presentation has been further improved as wel
Global gravitational instability of FLRW backgrounds - interpreting the dark sectors
The standard model of cosmology is based on homogeneous-isotropic solutions
of Einstein's equations. These solutions are known to be gravitationally
unstable to local inhomogeneous perturbations, commonly described as evolving
on a background given by the same solutions. In this picture, the FLRW
backgrounds are taken to describe the average over inhomogeneous perturbations
for all times. We study in the present article the (in)stability of FLRW dust
backgrounds within a class of averaged inhomogeneous cosmologies. We examine
the phase portraits of the latter, discuss their fixed points and orbital
structure and provide detailed illustrations. We show that FLRW cosmologies are
unstable in some relevant cases: averaged models are driven away from them
through structure formation and accelerated expansion. We find support for the
proposal that the dark components of the FLRW framework may be associated to
these instability sectors. Our conclusion is that FLRW cosmologies have to be
considered critically as for their role to serve as reliable models for the
physical background.Comment: 15 pages, 13 figures, 1 table. Matches published version in CQ
Lagrangian theory of structure formation in relativistic cosmology I: Lagrangian framework and definition of a nonperturbative approximation
In this first paper we present a Lagrangian framework for the description of
structure formation in general relativity, restricting attention to
irrotational dust matter. As an application we present a self-contained
derivation of a general-relativistic analogue of Zel'dovich's approximation for
the description of structure formation in cosmology, and compare it with
previous suggestions in the literature. This approximation is then
investigated: paraphrasing the derivation in the Newtonian framework we provide
general-relativistic analogues of the basic system of equations for a single
dynamical field variable and recall the first-order perturbation solution of
these equations. We then define a general-relativistic analogue of Zel'dovich's
approximation and investigate its implications by functionally evaluating
relevant variables, and we address the singularity problem. We so obtain a
possibly powerful model that, although constructed through extrapolation of a
perturbative solution, can be used to put into practice nonperturbatively, e.g.
problems of structure formation, backreaction problems, nonlinear properties of
gravitational radiation, and light-propagation in realistic inhomogeneous
universe models. With this model we also provide the key-building blocks for
initializing a fully relativistic numerical simulation.Comment: 21 pages, content matches published version in PRD, discussion on
singularities added, some formulas added, some rewritten and some correcte
On average properties of inhomogeneous fluids in general relativity II: perfect fluid cosmologies
For general relativistic spacetimes filled with an irrotational perfect fluid
a generalized form of Friedmann's equations governing the expansion factor of
spatially averaged portions of inhomogeneous cosmologies is derived. The
averaging problem for scalar quantities is condensed into the problem of
finding an `effective equation of state' including kinematical as well as
dynamical `backreaction' terms that measure the departure from a standard FLRW
cosmology. Applications of the averaged models are outlined including
radiation-dominated and scalar field cosmologies (inflationary and
dilaton/string cosmologies). In particular, the averaged equations show that
the averaged scalar curvature must generically change in the course of
structure formation, that an averaged inhomogeneous radiation cosmos does not
follow the evolution of the standard homogeneous-isotropic model, and that an
averaged inhomogeneous perfect fluid features kinematical `backreaction' terms
that, in some cases, act like a free scalar field source. The free scalar field
(dilaton) itself, modelled by a `stiff' fluid, is singled out as a special
inhomogeneous case where the averaged equations assume a simple form.Comment: TeX 21 pages, matches published version: G.R.G., in pres
Performance of the optimized Post-Zel'dovich approximation for CDM models in arbitrary FLRW cosmologies
We investigate the performance of the optimized Post-Zel'dovich approximation
in three cold dark matter cosmologies. We consider two flat models with
(SCDM) and with (CDM) and an open model
with (OCDM). We find that the optimization scheme proposed by
Wei{\ss}, Gottl\"ober & Buchert (1996), in which the performance of the
Lagrangian perturbation theory was optimized only for the Einstein-de Sitter
cosmology, shows the excellent performances not only for SCDM model but also
for both OCDM and CDM models. This universality of the excellent
performance of the optimized Post-Zel'dovich approximation is explained by the
fact that a relation between the Post-Zel'dovich order's growth factor
and Zel'dovich order's one , , is insensitive to the
background cosmologies.Comment: 8 pages, 3 figures, LaTex using aaspp4.sty and epsf.sty, Accepted for
publication in ApJ Letter
How is the local-scale gravitational instability influenced by the surrounding large-scale structure formation?
We develop the formalism to investigate the relation between the evolution of
the large-scale (quasi) linear structure and that of the small-scale nonlinear
structure in Newtonian cosmology within the Lagrangian framework. In doing so,
we first derive the standard Friedmann expansion law using the averaging
procedure over the present horizon scale. Then the large-scale (quasi) linear
flow is defined by averaging the full trajectory field over a large-scale
domain, but much smaller than the horizon scale. The rest of the full
trajectory field is supposed to describe small-scale nonlinear dynamics. We
obtain the evolution equations for the large-scale and small-scale parts of the
trajectory field. These are coupled to each other in most general situations.
It is shown that if the shear deformation of fluid elements is ignored in the
averaged large-scale dynamics, the small-scale dynamics is described by
Newtonian dynamics in an effective Friedmann-Robertson-Walker (FRW) background
with a local scale factor. The local scale factor is defined by the sum of the
global scale factor and the expansion deformation of the averaged large-scale
displacement field. This means that the evolution of small-scale fluctuations
is influenced by the surrounding large-scale structure through the modification
of FRW scale factor. The effect might play an important role in the structure
formation scenario. Furthermore, it is argued that the so-called {\it
optimized} or {\it truncated} Lagrangian perturbation theory is a good
approximation in investigating the large-scale structure formation up to the
quasi nonlinear regime, even when the small-scale fluctuations are in the
non-linear regime.Comment: 15pages, Accepted for publication in Gravitation and General
Relativit
Relative information entropy of an inhomogeneous universe
In the context of averaging an inhomogeneous cosmological model, we propose a
natural measure identical to the Kullback-Leibler relative information entropy,
which expresses the distinguishability of the local inhomogeneous density field
from its spatial average on arbitrary compact domains. This measure is expected
to be an increasing function in time and thus to play a significant role in
studying gravitational entropy. To verify this conjecture, we explore the time
evolution of the measure using the linear perturbation theory of a spatially
flat FLRW model and a spherically symmetric nonlinear solution. We discuss the
generality and conditions for the time-increasing nature of the measure, and
also the connection to the backreaction effect caused by inhomogeneities.Comment: 9 pages, 4 figures, LaTeX 2e using aipproc.cls, published in AIP
Conf. Proc., minor corrections mad
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