arXiv subjects

Thomas Buchert

Publications and source records attributed to Thomas Buchert.

At least 37 records · Page 2Linked to original sources

arXiv2019

Dynamical spatial curvature as a fit to type Ia supernovae

Few statements in cosmology can be made without assuming a cosmological model within which to interpret data. Statements about cosmic acceleration are no exception to this rule, and the inferred positive volume acceleration of our Universe often quoted in the literature is valid in the context of the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) class of space-times. Using the Joint Light-curve Analysis (JLA) catalogue of type Ia supernovae (SNIa), we examine the fit of a class of exact scaling solutions with dynamical spatial curvature formulated in the framework of a scalar averaging scheme for relativistic inhomogeneous space-times. In these models, global volume acceleration may emerge as a result of the non-local variance between expansion rates of clusters and voids, the latter gaining volume dominance in the late-epoch Universe. We find best-fit parameters for a scaling model of backreaction that are reasonably consistent with previously found constraints from SNIa, CMB, and baryon acoustic oscillations data. The quality of fit of the scaling solutions is indistinguishable from that of the LCDM model and the timescape cosmology from an Akaike Information Criterion (AIC) perspective. This indicates that a broad class of models can account for the $z\lesssim 1$ expansion history.

astro-ph.CO↗

arXiv2019

Dark Matter from Backreaction? Collapse models on galaxy cluster scales

In inhomogeneous cosmology, restricting attention to an irrotational dust matter model, backreaction arises in terms of the deviation of the averaged spatial scalar curvature from a constant-curvature model on some averaging domain $D$, $W_D$, and the kinematical backreaction $Q_D$. These backreaction variables can be modeled as an effective scalar field, called the `morphon field'. The general cosmological equations still need a closure condition to be solved. A simple example is the class of scaling solutions where $W_D$ and $Q_D$ are assumed to follow a power law of the volume scale factor $a_D$. But while they can describe models of quintessence, these and other models still assume the existence of dark matter in addition to the known sources. Going beyond scaling solutions by using a model for structure formation that we argue is reasonably generic, we investigate the correspondence between the morphon field and fundamental scalar field dark matter models, in order to describe dark matter as an effective phenomenon arising from kinematical backreaction and the averaged spatial curvature of the inhomogeneous Universe. While we find significant differences with those fundamental models, our main result is that the energy budget on typical collapsing domains is provided by curvature and matter in equal parts already around the turn-around time, leading to curvature dominance thereafter and increasing to a curvature contribution of $3/4$ of the energy budget at the onset of virialization. Kinematical backreaction is subdominant at early stages, but its importance rises quickly after turn-around and dominates the curvature contribution in the final phase of the collapse. We conclude that backreaction can indeed mimic dark matter (in the energy budget) during the collapse phase of megaparsec-scale structures.

gr-qc↗

arXiv2019

On the covariance of scalar averaging and backreaction in relativistic inhomogeneous cosmology

We introduce a generalization of the 4-dimensional averaging window function of Gasperini, Marozzi and Veneziano (2010) that may prove useful for a number of applications. The covariant nature of spatial scalar averaging schemes to address the averaging problem in relativistic cosmology is an important property that is implied by construction, but usually remains implicit. We employ here the approach of Gasperini et al. for two reasons. First, the formalism and its generalization presented here are manifestly covariant. Second, the formalism is convenient for disentangling the dependencies on foliation, volume measure, and boundaries in the averaged expressions entering in scalar averaging schemes. These properties will prove handy for simplifying expressions, but also for investigating extremal foliations and for comparing averaged properties of different foliations directly. The proposed generalization of the window function allows for choosing the most appropriate averaging scheme for the physical problem at hand, and for distinguishing between the role of the foliation itself and the role of the volume measure in averaged dynamic equations. We also show that one particular window function obtained from this generalized class results in an averaging scheme corresponding to that of a recent investigation by Buchert, Mourier and Roy (2018) and, as a byproduct, we explicitly show that the general equations for backreaction derived therein are covariant.

gr-qc↗

arXiv2019

Topology and Geometry of Gaussian random fields I: on Betti Numbers, Euler characteristic and Minkowski functionals

This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers $β_0$, $β_1$ and $β_2$. We show that Betti numbers entail a considerably richer characterization of the topology of the primordial density field. Of particular interest is that Betti numbers specify which topological features - islands, cavities or tunnels - define its spatial structure. A principal characteristic of Gaussian fields is that the three Betti numbers dominate the topology at different density ranges. At extreme density levels, the topology is dominated by a single class of features. At low levels this is a \emph{Swiss-cheeselike} topology, dominated by isolated cavities, at high levels a predominantly \emph{Meatball-like} topology of isolated objects. At moderate density levels, two Betti number define a more \emph{Sponge-like} topology. At mean density, the topology even needs three Betti numbers, quantifying a field consisting of several disconnected complexes, not of one connected and percolating overdensity. A {\it second} important aspect of Betti number statistics is that they are sensitive to the power spectrum. It reveals a monotonic trend in which at a moderate density range a lower spectral index corresponds to a considerably higher (relative) population of cavities and islands. We also assess the level of complementary information that Betti numbers represent, in addition to conventional measures such as Minkowski functionals. To this end, we include an extensive description of the Gaussian Kinematic Formula (GKF), which represents a major theoretical underpinning for this discussion.

astro-ph.CO↗

arXiv2018

Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background

We study the topology generated by the temperature fluctuations of the Cosmic Microwave Background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the LCDM paradigm with Gaussian distributed fluctuations. The survey of the CMB over $\mathbb{S}^2$ is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of "masks" is of importance, we introduce the concept of relative homology. The parametric $χ^2$-test shows differences between observations and simulations, yielding $p$-values at per-cent to less than per-mil levels roughly between 2 to 7 degrees. The highest observed deviation for $b_0$ and $b_1$ is approximately between $3σ$-4$σ$ at scales of 3 to 7 degrees. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66 degrees in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck's predecessor WMAP satellite. The mildly anomalous behaviour of Euler characteristic is related to the strongly anomalous behaviour of components and holes. These are also the scales at which the observed maps exhibit low variance compared to the simulations. Non-parametric tests show even stronger differences at almost all scales. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate to look at primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology.

astro-ph.CO↗

arXiv2018

Is Dark Energy Simulated by Structure Formation in the Universe ?

The standard model of cosmology assumes that the Universe can be described to hover around a homogeneous-isotropic solution of Einstein's general theory of relativity. This description needs (sometimes hidden) hypotheses that restrict the generality, and relaxing these restrictions is the headline of a new physical approach to cosmology that refurnishes the cosmological framework. Considering a homogeneous geometry as a template geometry for the in reality highly inhomogeneous Universe must be considered a strong idealization. Unveiling the limitations of the standard model opens the door to rich consequences of general relativity, giving rise to effective (i.e. spatially averaged) cosmological models that may even explain the longstanding problems of dark energy and dark matter. We explore in this talk the influence of structure formation on average properties of the Universe by discussing: (i) general thoughts on why considering average properties, on the key-issue of non-conserved curvature, and on the global gravitational instability of the standard model of cosmology; (ii) the general set of cosmological equations arising from averaging the scalar parts of Einstein's equations, the generic property of structure formation interacting with the average properties of the Universe in a scale-dependent way, and the description of cosmological backreaction in terms of an effective scalar field.

gr-qc↗

arXiv2018

Cosmological backreaction and its dependence on spacetime foliation

The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this letter an averaging formalism for the scalar parts of Einstein's equations that is coordinate-independent and only functionally depends on a metric. This formalism is applicable to general 3+1 foliations of spacetime for an arbitrary fluid with tilted flow. We clarify the dependence on spacetime foliation and argue that this dependence is weak in cosmological settings. We also introduce a new set of averaged equations that feature a global cosmological time despite the generality of the setting, and we put the statistical nature of effective cosmologies into perspective.

gr-qc↗

arXiv2018

Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids

We extend the general relativistic Lagrangian perturbation theory, recently developed for the formation of cosmic structures in a dust continuum, to the case of model universes containing a single fluid with a single-valued analytic equation of state. Using a coframe-based perturbation approach, we investigate evolution equations for structure formation in pressure-supported irrotational fluids that generate their rest-frame spacetime foliation. We provide master equations to first order for the evolution of the trace and traceless parts of barotropic perturbations that evolve in the perturbed space, where the latter describes the propagation of gravitational waves in the fluid. We illustrate the trace evolution for a linear equation of state and for a model equation of state describing isotropic velocity dispersion, and we discuss differences to the dust matter model, to the Newtonian case, and to standard perturbation approaches.

gr-qc↗

arXiv2017

Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of Lagrangian-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the Lagrangian perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.

gr-qc↗

arXiv2017

On Backreaction in Newtonian cosmology

We clarify that a result recently stated by Kaiser is contained in a theorem of Buchert and Ehlers that is widely known for its main result: that there is no global kinematical backreaction in Newtonian cosmology. Kaiser cites this paper, re-derives parts of the theorem, but incompletely restates its content. He makes further claims, which cannot be proven beyond the limited context of Newtonian cosmology. We also discuss recent papers of Rácz et al. and Roukema who claim the existence of global backreaction within the Newtonian framework.

astro-ph.CO↗

arXiv2017

Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski Functionals

Despite the wealth of $Planck$ results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependencies. Aiming at detecting the NGs of the CMB temperature anisotropy $δT$, while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function $P(δT)$, related to ${\mathrm v}_{0}$, the first Minkowski Functional (MF), and the two other MFs, ${\mathrm v}_{1}$ and ${\mathrm v}_{2}$. From their analytical Gaussian predictions we build the discrepancy functions $Δ_{k}$ ($k=P,0,1,2$) which are applied to an ensemble of $10^{5}$ CMB realization maps of the $Λ$CDM model and to the $Planck$ CMB maps. In our analysis we use general Hermite expansions of the $Δ_{k}$ up to the $12^{th}$ order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the $2^{nd}$ order expansions of Matsubara to arbitrary order in the standard deviation $σ_0$ for $P(δT)$ and ${\mathrm v}_0$, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the $Λ$CDM map sample and the $Planck$ data. We confirm the weak level of non-Gaussianity ($1$-$2$)$σ$ of the foreground corrected masked $Planck$ $2015$ maps.

astro-ph.CO↗

arXiv2017

Mass function of galaxy clusters in relativistic inhomogeneous cosmology

The current cosmological model ($Λ$CDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress--energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for more than $20$ years. Here we present one of the methods to tackle this problem, i.e. averaging the scalar parts of the Einstein equations, together with its application, the cosmological mass function of galaxy clusters.

astro-ph.CO↗

arXiv2017

Order-unity argument for structure-generated "extra" expansion

Self-consistent treatment of cosmological structure formation and expansion within the context of classical general relativity may lead to "extra" expansion above that expected in a structureless universe. We argue that in comparison to an early-epoch, extrapolated Einstein-de Sitter model, about 10-15% "extra" expansion is sufficient at the present to render superfluous the "dark energy" 68% contribution to the energy density budget, and that this is observationally realistic.

astro-ph.CO↗

arXiv2016

The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe

In relativistic inhomogeneous cosmology, structure formation couples to average cosmological expansion. A conservative approach to modelling this assumes an Einstein--de Sitter model (EdS) at early times and extrapolates this forward in cosmological time as a "background model" against which average properties of today's Universe can be measured. This requires adopting an early-epoch--normalised background Hubble constant $H_1^{bg}$. Here, we show that the $Λ$CDM model can be used as an observational proxy to estimate $H_1^{bg}$ rather than choose it arbitrarily. We assume (i) an EdS model at early times; (ii) a zero dark energy parameter; (iii) bi-domain scalar averaging---division of the spatial sections into over- and underdense regions; and (iv) virialisation (stable clustering) of collapsed regions. We find $H_1^{bg}= 37.7 \pm 0.4$ km/s/Mpc (random error only) based on a Planck $Λ$CDM observational proxy. Moreover, since the scalar-averaged expansion rate is expected to exceed the (extrapolated) background expansion rate, the expected age of the Universe should be much less than $2/(3 H_1^{bg}) = 17.3$ Gyr. The maximum stellar age of Galactic Bulge microlensed low-mass stars (most likely: 14.7 Gyr; 68\% confidence: 14.0--15.0 Gyr) suggests an age about a Gyr older than the (no-backreaction) $Λ$CDM estimate.

astro-ph.CO↗

arXiv2016

Observational Challenges for the Standard FLRW Model

We summarise some of the main observational challenges for the standard Friedmann-Lemaitre-Robertson-Walker cosmological model and describe how results recently presented in the parallel session `Large--scale Structure and Statistics' (DE3) at the `Fourteenth Marcel Grossman Meeting on General Relativity' are related to these challenges.

astro-ph.CO↗

arXiv2016

On the relativistic mass function and averaging in cosmology

The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.

astro-ph.CO↗

arXiv2016

Relativistic structure formation models and gravitoelectromagnetism

In the framework of Lagrangian perturbation theory in general relativity we discuss the possibility to split the Einstein equations, written in terms of spatial Cartan coframes within a 3+1 foliation of spacetime, into gravitoelectric and gravitomagnetic parts. While the former reproduces the full hierarchy of the Newtonian perturbation solutions, the latter contains non-Newtonian aspects like gravitational waves. This split can be understood and made unique through the Hodge decomposition of Cartan coframe fields.

gr-qc↗

arXiv2015

Is the baryon acoustic oscillation peak a cosmological standard ruler?

In the standard model of cosmology, the Universe is static in comoving coordinates; expansion occurs homogeneously and is represented by a global scale factor. The baryon acoustic oscillation (BAO) peak location is a statistical tracer that represents, in the standard model, a fixed comoving-length standard ruler. Recent gravitational collapse should modify the metric, rendering the effective scale factor, and thus the BAO standard ruler, spatially inhomogeneous. Using the Sloan Digital Sky Survey, we show to high significance (P < 0.001) that the spatial compression of the BAO peak location increases as the spatial paths' overlap with superclusters increases. Detailed observational and theoretical calibration of this BAO peak location environment dependence will be needed when interpreting the next decade's cosmological surveys.

astro-ph.CO↗