766 research outputs found

### 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

### 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

### 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

### Improving the Lagrangian perturbative solution for cosmic fluid: Applying Shanks transformation

We study the behavior of Lagrangian perturbative solutions. For a spherical
void model, the higher order the Lagrangian perturbation we consider, the worse
the approximation becomes in late-time evolution. In particular, if we stop to
improve until an even order is reached, the perturbative solution describes the
contraction of the void. To solve this problem, we consider improving the
perturbative solution using Shanks transformation, which accelerates the
convergence of the sequence. After the transformation, we find that the
accuracy of higher-order perturbation is recovered and the perturbative
solution is refined well. Then we show that this improvement method can apply
for a $\Lambda$CDM model and improved the power spectrum of the density field.Comment: 17 pages, 7 figures; accepted for publication in Phys.Rev.D; v2:
Evolution of power spectrum in LCDM model is added; v3: References are
correcte

### 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

### Effective inhomogeneous inflation: curvature inhomogeneities of the Einstein vacuum

We consider spatially averaged inhomogeneous universe models and argue that,
already in the absence of sources, an effective scalar field arises through
foliating and spatially averaging inhomogeneous geometrical curvature
invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an
inflaton, if we prescribe a potential of some generic form. We show that, for
any initially negative average spatial curvature, the morphon is driven through
an inflationary phase and leads - on average - to a spatially flat, homogeneous
and isotropic universe model, providing initial conditions for pre-heating and,
by the same mechanism, a possibly natural self-exit.Comment: 9 pages, 2 figures, to appear in Class. Quant. Grav. as Fast Track
Communicatio

### A cosmic equation of state for the inhomogeneous Universe: can a global far-from-equilibrium state explain Dark Energy?

A system of effective Einstein equations for spatially averaged scalar
variables of inhomogeneous cosmological models can be solved by providing a
`cosmic equation of state'. Recent efforts to explain Dark Energy focus on
`backreaction effects' of inhomogeneities on the effective evolution of
cosmological parameters in our Hubble volume, avoiding a cosmological constant
in the equation of state. In this Letter it is argued that, if kinematical
backreaction effects are indeed of the order of the averaged density (or larger
as needed for an accelerating domain of the Universe), then the state of our
regional Hubble volume would have to be in the vicinity of a
far-from-equilibrium state that balances kinematical backreaction and average
density. This property, if interpreted globally, is shared by a stationary
cosmos with effective equation of state $p_{\rm eff} = -1/3 \rho_{\rm eff}$. It
is concluded that a confirmed explanation of Dark Energy by kinematical
backreaction may imply a paradigmatic change of cosmology.Comment: 7 pages, matches published version in Class. Quant. Gra

### Beyond Zel'dovich-Type Approximations in Gravitational Instability Theory --- Pad\'e Prescription in Spheroidal Collapse ---

Among several analytic approximations for the growth of density fluctuations
in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate
scheme is known to be unusually accurate even in mildly non-linear regime. This
approximation is very similar to the Pad\'e approximation in appearance. We
first establish, however, that these two are actually different and independent
approximations with each other by using a model of spheroidal mass collapse.
Then we propose Pad\'e-prescribed Zel'dovich-type approximations and
demonstrate, within this model, that they are much accurate than any other
known nonlinear approximations.Comment: 4 pages, latex, 3 figures include

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