arXiv subjects

Thomas Buchert

Publications and source records attributed to Thomas Buchert.

At least 73 records · Page 4Linked to original sources

arXiv2010

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.

gr-qc↗

arXiv2010

Chaplygin gas and effective description of inhomogeneous universe models in general relativity

In the framework of spatially averaged inhomogeneous cosmologies in classical general relativity, effective Einstein equations govern the dynamics of averaged scalar variables in a scale--dependent way. A particular cosmology may be characterized by a cosmic equation of state, closing the hierarchy of effective equations. In this context a natural candidate is provided by the Chaplygin gas, standing for a unified description of dark energy and dark matter. In this paper, we suppose that the inhomogeneous properties of matter and geometry obey the Chaplygin equation of state. The most extreme interpretation assumes that both dark energy and dark matter are not included as additional sources, but are both manifestations of spatial geometrical properties. This feature is an important conceptual difference in comparison with the standard approach of a Friedmann-Lemaître-Robertson-Walker universe filled with dust and another fundamental field characterized by the Chaplygin equation of state. We finally discuss the consequences of the resulting scenario for effective cosmological parameters in order to establish the framework of a future confrontation with observations, and we note that the standard Chaplygin gas may not be ruled out by them.

gr-qc↗

arXiv2010

Multiscale cosmology and structure-emerging Dark Energy: A plausibility analysis

Cosmological backreaction suggests a link between structure formation and the expansion history of the Universe. In order to quantitatively examine this connection, we dynamically investigate a volume partition of the Universe into over-- and underdense regions. This allows us to trace structure formation using the volume fraction of the overdense regions $λ_{\CM}$ as its characterizing parameter. Employing results from cosmological perturbation theory and extrapolating the leading mode into the nonlinear regime, we construct a three--parameter model for the effective cosmic expansion history, involving $λ_{\CM_{0}}$, the matter density $Ω_{m}^{\CD_{0}}$, and the Hubble rate $H_{\CD_{0}}$ of today's Universe. Taking standard values for $Ω_{m}^{\CD_{0}}$ and $H_{\CD_{0}}$ as well as a reasonable value for $λ_{\CM_{0}}$, that we derive from $N$--body simulations, we determine the corresponding amounts of backreaction and spatial curvature. We find that the obtained values that are sufficient to generate today's structure also lead to a $Λ$CDM--like behavior of the scale factor, parametrized by the same parameters $Ω_{m}^{\CD_{0}}$ and $H_{\CD_{0}}$, but without a cosmological constant. However, the temporal behavior of $λ_{\CM}$ does not faithfully reproduce the structure formation history. Surprisingly, however, the model matches with structure formation with the assumption of a low matter content, $Ω_{m}^{\CD_{0}}\approx3\%$, a result that hints to a different interpretation of part of the backreaction effect as kinematical Dark Matter. (truncated)

astro-ph.CO↗

arXiv2009

On the Newtonian Limit of the Weyl Tensor

In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and magnetic parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system of equations in the Newtonian limit.

gr-qc↗

arXiv2009

Geometrical order-of-magnitude estimates for spatial curvature in realistic models of the Universe

The thoughts expressed in this article are based on remarks made by Jürgen Ehlers at the Albert-Einstein-Institut, Golm, Germany in July 2007. The main objective of this article is to demonstrate, in terms of plausible order-of-magnitude estimates for geometrical scalars, the relevance of spatial curvature in realistic models of the Universe that describe the dynamics of structure formation since the epoch of matter-radiation decoupling. We introduce these estimates with a commentary on the use of a quasi-Newtonian metric form in this context.

gr-qc↗

arXiv2008

Testing backreaction effects with observations

In order to quantitatively test the ability of averaged inhomogeneous cosmologies to correctly describe observations of the large scale properties of the Universe, we introduce a smoothed template metric corresponding to a constant spatial curvature model at any time, but with an evolving curvature parameter. This metric is used to compute quantities along an approximate effective lightcone of the averaged model of the Universe. As opposed to the standard Friedmann model, we parameterize this template metric by exact scaling properties of an averaged inhomogeneous cosmology, and we also motivate this form of the metric by results on a geometrical smoothing of inhomogeneous cosmological hypersurfaces. We test our hypothesis for the template metric against supernova data and the position of the CMB peaks, and infer the goodness--of--fit and parameter uncertainties. We find that averaged inhomogeneous models can reproduce the observations without requiring an additional Dark Energy component (though a volume acceleration is still needed), and that current data do not disfavour our main assumption on the effective lightcone structure. We also show that the experimental uncertainties on the angular diameter distance and the Hubble parameter from Baryon Acoustic Oscillations measurements -- forseen in future surveys like the proposed EUCLID satellite project -- are sufficiently small to distinguish between a FLRW template geometry and the template geometry with consistently evolving curvature. (Abridged)

astro-ph↗

arXiv2008

On the curvature of the present-day Universe

We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day Universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question whether it is sensible to assume that curvature averages out on some scale of homogeneity, as implied by the standard concordance model of cosmology, or whether the averaged scalar curvature can be largely negative today, as required for an explanation of Dark Energy from inhomogeneities. We confront both conjectures with a detailed analysis of the kinematical backreaction term and estimate its strength for a multi-scale inhomogeneous matter and curvature distribution. Our main result is a formula for the spatially averaged scalar curvature involving quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. We propose strategies to quantitatively evaluate the formula, and pinpoint the assumptions implied by the conjecture of a small or zero averaged curvature. We reach the conclusion that the standard concordance model needs fine-tuning in the sense of an assumed equipartition law for curvature in order to reconcile it with the estimated properties of the averaged physical space, whereas a negative averaged curvature is favoured, independent of the prior on the value of the cosmological constant.

gr-qc↗

arXiv2008

Ricci flow deformation of cosmological initial data sets

Ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes. This idea has been around since the appearance of the Ricci flow on the scene, but it has been difficult to turn it into a sound mathematical procedure. In this expository talk we illustrate, how Perelman's recent results in Ricci flow theory can considerably improve on such a situation. From a physical point of view this analysis can be related to the issue of finding a constant-curvature template spacetime for the inhomogeneous Universe, relevant to the interpretation of observational data and, hence, bears relevance to the dark energy and dark matter debates. These techniques provide control on curvature fluctuations (intrinsic backreaction terms) in their relation to the averaged matter distribution.

math-ph↗

arXiv2007

Dark Energy from structure: a status report

The effective evolution of an inhomogeneous universe model in any theory of gravitation may be described in terms of spatially averaged variables. In Einstein's theory, restricting attention to scalar variables, this evolution can be modeled by solutions of a set of Friedmann equations for an effective volume scale factor, with matter and backreaction source terms. The latter can be represented by an effective scalar field (`morphon field') modeling Dark Energy. The present work provides an overview over the Dark Energy debate in connection with the impact of inhomogeneities, and formulates strategies for a comprehensive quantitative evaluation of backreaction effects both in theoretical and observational cosmology. We recall the basic steps of a description of backreaction effects in relativistic cosmology that lead to refurnishing the standard cosmological equations, but also lay down a number of challenges and unresolved issues in connection with their observational interpretation. The present status of this subject is intermediate: we have a good qualitative understanding of backreaction effects pointing to a global instability of the standard model of cosmology; exact solutions and perturbative results modeling this instability lie in the right sector to explain Dark Energy from inhomogeneities. It is fair to say that, even if backreaction effects turn out to be less important than anticipated by some researchers, the concordance high-precision cosmology, the architecture of current N-body simulations, as well as standard perturbative approaches may all fall short in correctly describing the Late Universe.

gr-qc↗

arXiv2007

Backreaction Issues in Relativistic Cosmology and the Dark Energy Debate

The effective evolution of an inhomogeneous universe model in Einstein's theory of gravitation may be described in terms of spatially averaged scalar variables. This evolution can be modeled by solutions of a set of Friedmann equations for an effective scale factor, with matter and backreaction source terms, where the latter can be represented by a minimally coupled scalar field (`morphon field'). We review the basic steps of a description of backreaction effects in relativistic cosmology that lead to refurnishing the standard cosmological equations, but also lay down a number of unresolved issues in connection with their interpretation within observational cosmology.

gr-qc↗

arXiv2006

Reinterpreting dark energy through backreaction: the minimally coupled morphon field

In the context of averaged cosmologies, the effective equations can be written in the form of "regional" Friedmannian equations with additional sources arising from the so-called backreaction of inhomogeneities. We propose a mean field description of this backreaction in terms of a regionally homogeneous scalar field: this provides a physical motivation to the phenomenological scalar fields generically called quintessence fields. We explicitly reconstruct the potential of the scalar field for a one-parameter family of scaling solutions to the backreaction problem, showing that it entails most of the standard scalar fields including e.g. standard and phantom quintessence scenarii.

astro-ph↗

arXiv2006

Correspondence between kinematical backreaction and scalar field cosmologies - the `morphon field'

Spatially averaged inhomogeneous cosmologies in classical general relativity can be written in the form of effective Friedmann equations with sources that include backreaction terms. In this paper we propose to describe these backreaction terms with the help of a homogeneous scalar field evolving in a potential; we call it the `morphon field'. This new field links classical inhomogeneous cosmologies to scalar field cosmologies, allowing to reinterpret, e.g., quintessence scenarios by routing the physical origin of the scalar field source to inhomogeneities in the Universe. We investigate a one-parameter family of scaling solutions to the backreaction problem. Subcases of these solutions (all without an assumed cosmological constant) include scale-dependent models with Friedmannian kinematics that can mimic the presence of a cosmological constant or a time-dependent cosmological term. We explicitly reconstruct the scalar field potential for the scaling solutions, and discuss those cases that provide a solution to the Dark Energy and coincidence problems. In this approach, Dark Energy emerges from morphon fields, a mechanism that can be understood through the proposed correspondence: the averaged cosmology is characterized by a weak decay (quintessence) or growth (phantom quintessence) of kinematical fluctuations, fed by `curvature energy' that is stored in the averaged 3-Ricci curvature. We find that the late-time trajectories of those models approach attractors that lie in the future of a state that is predicted by observational constraints.

gr-qc↗

arXiv2006

Reinterpreting quintessential dark energy through averaged inhomogeneous cosmologies

Regionally averaged relativistic cosmologies have recently been considered as a possible explanation for the apparent late time acceleration of the Universe. This contribution reports on a mean field description of the backreaction in terms of a minimally coupled regionally homogeneous scalar field evolving in a potential, then giving a physical origin to the various phenomenological scalar fields generically called quintessence fields. As an example, the correspondence is then applied to scaling solutions.

astro-ph↗

arXiv2006

The non-perturbative regime of cosmic structure formation

This paper focusses on the barely understood gap between the weakly nonlinear regime of structure formation and the onset of the virialized regime. While the former is accessed through perturbative calculations and the latter through virialization conditions incorporating dynamical stresses that arise in collisionless self-gravitating systems due to velocity dispersion forces, the addressed regime can only be understood through non-perturbative models. We here present an exact Lagrangian integral that provides a tool to access this regime. We derive a transport equation for the peculiar-gravitational field strength and integrate it along comoving trajectories of fluid elements. The so-obtained integral provides an exact expression that solves the longitudinal gravitational field equation in general. We argue that this integral provides a powerful approximation beyond the Lagrangian perturbative regime, and discuss its relation to known approximations, among them Lagrangian perturbation solutions including the Zel'dovich approximation and approximations for adhesive gravitational clustering, including the adhesion approximation. Furthermore, we propose an iteration scheme for a systematic analytical and numerical construction of trajectory fields. The integral may also be employed to improve inverse reconstruction techniques.

astro-ph↗

arXiv2006

An exact Lagrangian integral for the Newtonian gravitational field strength

An exact expression for the gravitational field strength in a self-gravitating dust continuum is derived within the Lagrangian picture of continuum mechanics. From the Euler-Newton system a transport equation for the gravitational field strength is formulated and then integrated along trajectories of continuum elements. The resulting integral solves one of the Lagrangian equations of the corresponding Lagrange-Newton system in general. Relations to known exact solutions without symmetry in Newtonian gravity are discussed. The presented integral may be employed to access the non-perturbative regime of structure formation in Newtonian cosmology, and to apply iterative Lagrangian schemes to solve the Lagrange-Newton system.

gr-qc↗

arXiv2005

On globally static and stationary cosmologies with or without a cosmological constant and the Dark Energy problem

In the framework of spatially averaged inhomogeneous cosmologies in classical General Relativity, effective Einstein equations govern the regional and the global dynamics of averaged scalar variables of cosmological models. A particular solution may be characterized by a cosmic equation of state. In this paper it is pointed out that a globally static averaged dust model is conceivable without employing a compensating cosmological constant. Much in the spirit of Einstein's original model we discuss consequences for the global, but also for the regional properties of this cosmology. We then consider the wider class of globally stationary cosmologies that are conceivable in the presented framework. All these models are based on exact solutions of the averaged Einstein equations and provide examples of cosmologies in an out-of-equilibrium state, which we characterize by an information-theoretical measure. It is shown that such cosmologies preserve high-magnitude kinematical fluctuations and so tend to maintain their global properties. The same is true for a $Λ-$driven cosmos in such a state despite of exponential expansion. We outline relations to inflationary scenarios, and put the Dark Energy problem into perspective. Here, it is argued, on the grounds of the discussed cosmologies, that a classical explanation of Dark Energy through backreaction effects is theoretically conceivable, if the matter-dominated Universe emerged from a non-perturbative state in the vicinity of the stationary solution. We also discuss a number of caveats that furnish strong counter arguments in the framework of structure formation in a perturbed Friedmannian model.

gr-qc↗

arXiv2005

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 $p_{\rm eff} = -1/3 ρ_{\rm eff}$. It is concluded that a confirmed explanation of Dark Energy by kinematical backreaction may imply a paradigmatic change of cosmology.

gr-qc↗

arXiv2005

Adhesive Gravitational Clustering

The notion of `adhesion' has been advanced for the phenomenon of stabilization of large-scale structure emerging from gravitational instability of a cold medium. Recently, the physical origin of adhesion has been identified: a systematic derivation of the equations of motion for the density and the velocity fields leads naturally to the key equation of the `adhesion approximation' - however, under a set of strongly simplifying assumptions. In this work, we provide an evaluation of the current status of adhesive gravitational clustering and a clear explanation of the assumptions involved. Furthermore, we propose systematic generalizations with the aim to relax some of the simplifying assumptions. We start from the general Newtonian evolution equations for self-gravitating particles on an expanding Friedmann background and recover the popular `dust model' (pressureless fluid), which breaks down after the formation of density singularities; then we investigate, in a unified framework, two other models which, under the restrictions referred to above, lead to the `adhesion approximation'. We apply the Eulerian and Lagrangian perturbative expansions to these new models and, finally, we discuss some non-perturbative results that may serve as starting points for workable approximations of non-linear structure formation in the multi-stream regime. In particular, we propose a new approximation that includes, in limiting cases, the standard `adhesion model' and the Eulerian as well as Lagrangian first-order approximations.

astro-ph↗