arXiv subjects

Thomas Buchert

Publications and source records attributed to Thomas Buchert.

At least 91 records · Page 5Linked to original sources

arXiv2005

Minkowski Functionals of SDSS galaxies I : Analysis of Excursion Sets

We present a first morphometric investigation of a preliminary sample from the SDSS of 154287 galaxies with apparent magnitude 14.5<m_r<17.5 and redshift 0.001<z<0.4. We measure the Minkowski Functionals, which are a complete set of morphological descriptors. To account for the complicated wedge--like geometry of the present survey data, we construct isodensity contour surfaces from the galaxy positions in redshift space and employ two complementary methods of computing the Minkowski Functionals. We find that the observed Minkowski Functionals for SDSS galaxies are consistent with the prediction of a Lambda--dominated spatially--flat Cold Dark Matter model with random--Gaussian initial conditions, within the cosmic variance estimated from the corresponding mock catalogue. We expect that future releases of the SDSS survey will allow us to distinguish morphological differences in the galaxy distribution with regard to different morphological type and luminosity ranges.

astro-ph↗

arXiv2004

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.

gr-qc↗

arXiv2003

The Cosmic Quartet - Cosmological Parameters of a Smoothed Inhomogeneous Spacetime

We discuss the relation between `bare' cosmological parameters as the true spatial average characteristics that determine the cosmological model, and the parameters interpreted by observers with a `Friedmannian bias', i.e., within a homogeneous space geometry. We may say that the latter are `dressed' by the smoothed-out geometrical inhomogeneities of the surveyed spatial region. We identify two effects that quantify the difference between `bare' and `dressed' parameters: `curvature backreaction' and `volume effect'. An estimate of the latter is given in terms of a simple geometrical example.

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arXiv2003

Universality in the distribution of caustics in the expanding Universe

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals of caustic appearances and the spatial distribution of caustics at subsequent times, we find that the time--intervals of caustic appearances approach a constant, i.e., their time--subsequent ratio converges to 1; it is also found that the spatial distribution of caustics at a given time features some universality rules, e.g., the ratio between the position of the nearest caustic from the center and that of the second nearest caustic from the center approaches a constant. Furthermore we find some rules for the mass distribution for each caustic. Using these universality constants we are in the position to predict the spatial distribution of caustics at an arbitrary time in order to give an estimate for the power spectral index in the fully--developed non--dissipative turbulent (`virialized') regime.

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arXiv2002

Regional averaging and scaling in relativistic cosmology

Averaged inhomogeneous cosmologies lie at the forefront of interest, since cosmological parameters like the rate of expansion or the mass density are to be considered as volume-averaged quantities and only these can be compared with observations. For this reason the relevant parameters are intrinsically scale-dependent and one wishes to control this dependence without restricting the cosmological model by unphysical assumptions. In the latter respect we contrast our way to approach the averaging problem in relativistic cosmology with shortcomings of averaged Newtonian models. Explicitly, we investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian smoothing of (tensorial) variables as opposed to their Eulerian averaging on spatial domains. This program is realized with the help of a global Ricci deformation flow for the metric. We explain rigorously the origin of the Ricci flow which, on heuristic grounds, has already been suggested as a possible candidate for smoothing the initial data set for cosmological spacetimes. The smoothing of geometry implies a renormalization of averaged spatial variables. We discuss the results in terms of effective cosmological parameters that would be assigned to the smoothed cosmological spacetime.

gr-qc↗

arXiv2002

Cosmological parameters are dressed

In the context of the averaging problem in relativistic cosmology, we provide a key to the interpretation of cosmological parameters by taking into account the actual inhomogeneous geometry of the Universe. We discuss the relation between `bare' cosmological parameters determining the cosmological model, and the parameters interpreted by observers with a ``Friedmannian bias'', which are `dressed' by the smoothed-out geometrical inhomogeneities of the surveyed spatial region.

gr-qc↗

arXiv2001

On the abundance of collapsed objects

The redshift dependence of the abundance of collapsed objects places strong constraints on cosmological models of structure formation. We apply a recently proposed model describing the anisotropic collapse of inhomogeneous spatial domains. Compared with the spherical top-hat model, this generic model leads to significantly more collapsed objects at high redshifts: at redshift one and on the scale of rich clusters a factor of 65. Furthermore, for a fixed normalization of the initial fluctuation spectrum (σ_8=1), we predict four times as much presently collapsed objects on the mass-scale of rich clusters within the standard CDM cosmogony, compared to the spherical collapse.

astro-ph↗

arXiv2001

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.

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arXiv2001

Matter seen at many scales and the geometry of averaging in relativistic cosmology

We investigate the scale-dependence of Eulerian volume averages of scalar functions on Riemannian three-manifolds. We propose a complementary view of a Lagrangian scaling of variables as opposed to their Eulerian averaging on spatial domains. This program explains rigorously the origin of the Ricci deformation flow for the metric, a flow which, on heuristic grounds, has been already suggested as a possible candidate for averaging the initial data set for cosmological spacetimes.

gr-qc↗

arXiv2000

Backreaction of inhomogeneities on the expansion: the evolution of cosmological parameters

Averaging and evolving inhomogeneities are non-commuting operations. This implies the existence of deviations of an averaged model from the standard Friedmann-Lemaitre cosmologies. We quantify these deviations, encoded in a backreaction parameter, in the framework of Newtonian cosmology. We employ the linear theory of gravitational instability in the Eulerian and Lagrangian approaches, as well as the spherically- and plane-symmetric solutions as standards of reference. We propose a model for the evolution of the average characteristics of a spatial domain for generic initial conditions that contains the spherical top-hat model and the planar collapse model as exact sub cases. A central result is that the backreaction term itself, calculated on sufficiently large domains, is small but, still, its presence can drive the cosmological parameters on the averaging domain far away from their global values of the standard model. We quantify the variations of these parameters in terms of the fluctuations in the initial data as derived from the power spectrum of initial cold dark matter density fluctuations. E.g. in a domain with a radius of 100Mpc today and initially one-sigma fluctuations, the density parameters deviate from their homogeneous values by 15%; three-sigma fluctuations lead to deviations larger than 100%.

astro-ph↗

arXiv2000

On average properties of inhomogeneous cosmologies

The present talk summarizes the recently progressed state of a systematic re-evaluation of cosmological models that respect the presence of inhomogeneities. Emphasis is given to identifying the basic steps towards an effective (i.e. spatially averaged) description of structural evolution, also unfolding the various facets of a `smoothed--out' cosmology. We shall highlight some results obtained within Newtonian cosmology, discuss expansion laws in general relativity within a covariant fluid approach, and put forward some promising directions of future research.

gr-qc↗

arXiv1999

On average properties of inhomogeneous fluids in general relativity I: dust cosmologies

For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law governing a generic domain can be found. However, as the general equations show, `backreaction' acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.

gr-qc↗

arXiv1999

Stabilization of Large Scale Structure by Adhesive Gravitational Clustering

The interplay between gravitational and dispersive forces in a multi-streamed medium leads to an effect which is exposed in the present note as the genuine driving force of stabilization of large-scale structure. The conception of `adhesive gravitational clustering' is advanced to interlock the fairly well-understood epoch of formation of large-scale structure and the onset of virialization into objects that are dynamically in equilibrium with their large-scale structure environment. The classical `adhesion model' is opposed to a class of more general models traced from the physical origin of adhesion in kinetic theory.

astro-ph↗

arXiv1999

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.

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arXiv1999

Backreaction in Cosmological Models

Most cosmological models studied today are based on the assumption of homogeneity and isotropy. Observationally one can find evidence that supports these assumptions on very large scales, the strongest being the almost isotropy of the Cosmic Microwave Background radiation after assigning the whole dipole to our proper motion relative to this background. However, on small and on intermediate scales up to several hundreds of Mpcs, there are strong deviations from homogeneity and isotropy. Here the problem arises how to relate the observations with the homogeneous and isotropic models. The usual proposal for solving this problem is to assume that Friedmann-Lemaitre models describe the mean observables. Such mean values may be identified with spatial averages. For Newtonian fluid dynamics the averaging procedure has been discussed in detail in Buchert and Ehlers (1997), leading to an additional backreaction term in the Friedmann equation. We use the Eulerian linear approximation and the `Zel'dovich approximation' to estimate the effect of the backreaction term on the expansion. Our results indicate that even for domains matching the background density in the mean, the evolution of the scale factor strongly deviates from the Friedmann solution, critically depending on the velocity field inside.

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arXiv1999

Extending the scope of models for large-scale structure formation in the Universe

We propose a phenomenological generalization of the models of large-scale structure formation in the Universe by gravitational instability in two ways: we include pressure forces to model multi-streaming, and noise to model fluctuations due to neglected short-scale physical processes. We show that pressure gives rise to a viscous-like force of the same character as that one introduced in the ``adhesion model'', while noise leads to a roughening of the density field yielding a scaling behavior of its correlations.

astro-ph↗

arXiv1999

The fundamental plane of clusters of galaxies: a quest for understanding cluster dynamics and morphology

We discuss implications of the fundamental plane parameters of clusters of galaxies derived from combined optical and X-ray data of a sample of 78 nearby clusters. In particular, we investigate the dependence of these parameters on the dynamical state of the cluster. We introduce a new concept of allocation of the fundamental plane of clusters derived from their intrinsic morphological properties, and put some theoretical implications of the existence of a fundamental plane into perspective.

astro-ph↗

arXiv1999

Lagrangian theory of structure formation in pressure-supported cosmological fluids

The Lagrangian theory of structure formation in cosmological fluids, restricted to the matter model ``dust'', provides successful models of large-scale structure in the Universe in the laminar regime, i.e., where the fluid flow is single-streamed and ``dust''-shells are smooth. Beyond the epoch of shell-crossing a qualitatively different behavior is expected, since in general anisotropic stresses powered by multi-stream forces arise in collisionless matter. In this paper we provide the basic framework for the modeling of pressure-supported fluids, thus restricting attention to isotropic stresses and to the cases where pressure can be given as a function of the density. We derive the governing set of Lagrangian evolution equations and study the resulting system using Lagrangian perturbation theory. We discuss the first-order equations and compare them to the Eulerian theory of gravitational instability, as well as to the case of plane-symmetric collapse. We obtain a construction rule that allows to derive first-order solutions of the Lagrangian theory from known first-order solutions of the Eulerian theory and so extend Zel'dovich's extrapolation idea into the multi-streamed regime. These solutions can be used to generalize current structure formation models in the spirit of the ``adhesion approximation''.

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