arXiv subjects

Thomas Buchert

Publications and source records attributed to Thomas Buchert.

At least 19 recordsLinked to original sources

arXiv2026

Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood

We present the first direct computation of spatially averaged dynamical quantities in the local Universe, employing the Cosmicflows-4++ reconstruction and a covariant scalar averaging formalism. We extract the domain-averaged density, expansion rate, spatial curvature, and kinematical backreaction over cosmologically relevant domains around our Galaxy, extending up to a comoving radius of $300~\mathrm{Mpc}/h$. The resulting domain-averaged present-day energy budget features nontrivial variations with scale that reflect a nested structure within the cosmic neighborhood, including a large-scale void shell encompassing the local cosmic web. Remarkably, we find significant contributions to this energy budget from the average spatial curvature at the $\mathcal{O}(10\%)$ level on all probed scales. By contrast, the kinematical backreaction remains much smaller throughout the surveyed volume, reaching at most a $\mathcal{O}(1\%)$ contribution on the smallest scales considered, i.e., $30~\mathrm{Mpc}/h$. Convergence to the global $\Lambda$CDM background is not observed within this range of scales.

astro-ph.CO↗

arXiv2026

Novel Realizations of Warp Drive Spacetimes as Solutions of General Relativity

We first take a closer look at the original warp drive proposal by Alcubierre, examine its kinematics in the context of a covariant 3+1 setting, and explain some drawbacks of this construction. In this model, changes of the velocity profile are suppressed, apart from an externally given amplitude. We then discuss Einstein's equations for currently employed spacetime restrictions, and provide the governing equations for the Nat\'ario class of metrics with one-component coordinate velocity in a subcase. Following Synge's G-method we determine the constraints on realizations for two examples: assuming the form of the solution a priori as in Alcubierre's model, and determining the solution through an assumption imposed along geodesics. We analyze in detail the role of coordinate acceleration and coordinate vorticity, providing illustrations for both example solutions. For the second we find an expected generic instability of the warp field. We then propose a framework that allows for spatial curvature and the description of warp field dynamics within a relativistic Lagrangian perturbation approach, also including exact solutions of the Szekeres class II. These generalizations allow us to link studies on warp fields to relativistic cosmology. A direct correspondence between solutions of Newtonian gravity and general relativity is exploited. We conclude by discussing possible future paths towards physical warp drives within tilted fluid flows.

gr-qc↗

arXiv2026

General formalism, classification, and demystification of the current warp-drive spacetimes

We critically examine proposals for the so-called warp-drive spacetimes and classify these models based on their various restrictions within the framework of General Relativity. We then provide a summary of general formalism for each class, and in the process, we highlight some misconceptions, misunderstandings, and errors in the literature that have been used to support claims about the physicality and feasibility of these models. On the way, we prove several new no-go theorems. Our analysis shows that when the principles of General Relativity are applied correctly, most claims regarding physical warp drives must be reassessed, and it becomes highly challenging to justify or support the viability of such models, not merely due to the violation of energy conditions.

gr-qc↗

arXiv2024

On restrictions of current warp drive spacetimes and immediate possibilities of improvement

Looking at current proposals of so-called `warp drive spacetimes', they appear to employ General Relativity only at an elementary level. A number of strong restrictions are imposed such as flow-orthogonality of the spacetime foliation, vanishing spatial Ricci tensor, dimensionally reduced and coordinate-dependent velocity fields, to mention the main restrictions. We here provide a brief summary of our proposal of a general and covariant description of spatial motions within General Relativity, then discuss the restrictions that are employed in the majority of the current literature. That current warp drive models are discussed to be unphysical may not be surprising; they lack important ingredients such as covariantly non-vanishing spatial velocity, acceleration, vorticity, together with curved space, and a warp mechanism.

gr-qc↗

arXiv2023

Direct correspondence between Newtonian gravitation and general relativity

We present a strategy to obtain equations of general relativity for an irrotational dust continuum within a flow-orthogonal foliation of spacetime from the equations of Newtonian gravitation, and vice versa, without employing a weak field expansion or a limiting process on the speed of light. We argue that writing Newton's equations in a Lagrangian frame and relaxing integrability of vector gradients is sufficient to obtain equations that are identical to Einstein's equations in (3+1)-form when respecting the Lorentzian signature of the time parametrization. We discuss implications and provide an outlook on how to extend the obtained correspondence to more general spacetimes.

gr-qc↗

arXiv2023

Nonperturbative collapse models for collisionless self-gravitating flows

Structure formation in the Universe has been well-studied within the Eulerian and Lagrangian perturbation theories, where the latter performs substantially better in comparison with N-body simulations. Standing out is the celebrated Zel'dovich approximation for dust matter. In this work, we recall the description of gravitational noncollisional systems and extend both the Eulerian and Lagrangian approaches by including, possibly anisotropic, velocity dispersion. A simple case with plane symmetry is then studied with an exact, nonperturbative approach, and various approximations of the derived model are then compared numerically. A striking result is that linearized Lagrangian solutions outperform models based on Burgers' equation in the multistream regime in comparison with the exact solution. These results are finally extended to a 3D case without symmetries, and master equations for the evolution of all parts of the perturbations are derived. The particular 3D case studied corresponds to a maximally anisotropic collapse, which involves an approximation based on the estimation of importance of the different levels of spatial derivatives of the local deformation field.

astro-ph.CO↗

arXiv2023

Homology reveals significant anisotropy in the cosmic microwave background

We test the tenet of statistical isotropy of the standard cosmological model via a homology analysis of the cosmic microwave background temperature maps. Examining small sectors of the normalized maps, we find that the results exhibit a dependence on whether we compute the mean and variance locally from the masked patch, or from the full masked sky. Assigning local mean and variance for normalization, we find the maximum discrepancy between the data and model in the galactic northern hemisphere at more than $3.5$ s.d. for the PR4 dataset at degree-scale. For the PR3 dataset, the C-R and SMICA maps exhibit higher significance than the PR4 dataset at $\sim 4$ and $4.1$ s.d. respectively, however the NILC and SEVEM maps exhibit lower significance at $\sim 3.4$ s.d. The southern hemisphere exhibits high degree of consistency between the data and the model for both the PR4 and PR3 datasets. Assigning the mean and variance of the full masked sky decreases the significance for the northern hemisphere, the tails in particular. However the tails in the southern hemisphere are strongly discrepant at more than $4$ standard deviations at approximately $5$ degrees. The $p$-values obtained from the $\chi^2$-statistic exhibit commensurate significance in both the experiments. Examining the quadrants of the sphere, we find the first quadrant to be the major source of the discrepancy. Prima-facie, the results indicate a breakdown of statistical isotropy in the CMB maps, however more work is needed to ascertain the source of the anomaly. Regardless, these map characteristics may have serious consequences for downstream computations such as parameter estimation, and the related Hubble tension.

astro-ph.CO↗

arXiv2023

Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation

We develop a new nonlinear method to model structure formation in general relativity from a generalization of the relativistic Lagrangian perturbation schemes, controlled by Szekeres (and LTB) exact solutions. The overall approach can be interpreted as the evolution of a deformation field on an inhomogeneous reference model, obeying locally Friedmann-like equations. In the special case of locally one-dimensional deformations, the new model contains the entire Szekeres family of exact solutions. As thus formulated, this approach paraphrases the Newtonian and relativistic Zel'dovich approximations, having a large potential for applications in contexts where relativistic degrees of freedom are relevant. Numerical simulations are implemented to illustrate the capabilities and accuracy of the model.

gr-qc↗

arXiv2022

The averaging problem on the past null cone in inhomogeneous dust cosmologies

Cosmological models typically neglect the complicated nature of the spacetime manifold at small scales in order to hypothesize idealized general relativistic solutions for describing the average dynamics of the Universe. Although these solutions are remarkably successful in accounting for data, they introduce a number of puzzles in cosmology, and their foundational assumptions are therefore important to test. In this paper, we go beyond the usual assumptions in cosmology and propose a formalism for averaging the local general relativistic spacetime on an observer's past null cone: we formulate average properties of light fronts as they propagate from a cosmological emitter to an observer. The energy-momentum tensor is composed of an irrotational dust source and a cosmological constant -- the same components as in the $Λ$CDM model for late cosmic times -- but the metric solution is not \emph{a priori}constrained to be locally homogeneous or isotropic. This generally makes the large-scale dynamics depart from that of a simple Friedmann--Lema\^ıtre--Robertson--Walker solution through \emph{backreaction} effects. Our formalism quantifies such departures through a fully covariant system of area-averaged equations on the light fronts propagating towards an observer, which can be directly applied to analytical and numerical investigations of cosmic observables. For this purpose, we formulate light front averages of observable quantities, including the effective angular diameter distance and the cosmological redshift drift and we also discuss the backreaction effects for these observables.

gr-qc↗

arXiv2022

On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization

The Newtonian Lagrangian perturbation theory is a widely used framework to study structure formation in cosmology in the nonlinear regime. We review a general-relativistic formulation of such a perturbation approach, emphasizing results on already developed extensive formalism including among other aspects: the non-perturbative modeling of Ricci and Weyl curvatures, gravitational waves and pressure-supported fluids. We discuss subcases of exact solutions related to Szekeres Class II and, as exact average model, Ricci-flat LTB models. This latter forms the basis of a generalization that we then propose in terms of a scheme that goes beyond the relativistic Lagrangian perturbation theory on a global homogeneous-isotropic background cosmology. This new approximation does not involve a homogeneous reference background and it contains Szekeres class I (and thus general LTB models) as exact subcases. Most importantly, this new approximation allows for the interaction of structure with an evolving `background cosmology', conceived as a spatial average model, and thus includes cosmological backreaction.

gr-qc↗

arXiv2022

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $σ_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,σ$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $Ω_m$, and the amplitude or rate of the growth of structure ($σ_8,fσ_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged]

astro-ph.CO↗

arXiv2021

The variance of the CMB temperature gradient: a new signature of a multiply connected Universe

In this work we investigate the standard deviation of the Cosmic Microwave Background (CMB) temperature gradient field as a signature for a multiply connected nature of the Universe. CMB simulations of a spatially infinite universe model within the paradigm of the standard cosmological model present non-zero two-point correlations at any angular scale. This is in contradiction with the extreme suppression of correlations at scales above $60^{\circ}$ in the observed CMB maps. Universe models with spatially multiply connected topology contain typically a discrete spectrum of the Laplacian with a specific wave-length cut-off and thus lead to a suppression of the correlations at large angular scales, as observed in the CMB (in general there can be also an additional continuous spectrum). Among the simplest examples are 3-dimensional tori which possess only a discrete spectrum. To date, the universe models with non-trivial topology such as the toroidal space are the only models that possess a two-point correlation function showing a similar behaviour as the one derived from the observed Planck CMB maps. In this work it is shown that the normalized standard deviation of the CMB temperature gradient field does hierarchically detect the change in size of the cubic 3-torus, if the volume of the Universe is smaller than $\simeq 2.5 \cdot 10^3$ Gpc$^3$. It is also shown that the variance of the temperature gradient of the Planck maps is consistent with the median value of simulations within the standard cosmological model. All flat tori are globally homogeneous, but are globally anisotropic. However, this study also presents a test showing a level of homogeneity and isotropy of all the CMB map ensembles for the different torus sizes considered that are nearly at the same weak level of anisotropy revealed by the CMB in the standard cosmological model.

astro-ph.CO↗

arXiv2021

Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?

We present measurements of the Minkowski functionals extracted from the SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe how an unbiased reconstruction of these statistics can be obtained from a field with masked regions and survey boundaries, validating our methodology with Gaussian random fields and mock galaxy snapshot data. From the BOSS galaxy data we generate a set of four density fields in three dimensions corresponding to the northern and southern skies of LOWZ and CMASS catalogs, smoothing over large scales such that the field is perturbatively non-Gaussian. We extract the Minkowski functionals from each data set separately, and measure their shapes and amplitudes by fitting a Hermite polynomial expansion. For the shape parameter of the Minkowski functional curves $a_0$, that is related to the bispectrum of the field, we find that the LOWZ-South data presents a systematically lower value of $a_0 = -0.080 \pm 0.040$ than its northern sky counterpart $a_0 = 0.032 \pm 0.024$. Although the significance of this discrepancy is low, it potentially indicates some systematics in the data or that the matter density field exhibits anisotropy at low redshift. By assuming a standard isotropic flat $Λ$CDM cosmology, the amplitudes of Minkowski functionals from the combination of northern and southern sky data give the constraints $Ω_{\rm c} h^2 n_{\rm s} = 0.110 \pm 0.006$ and $0.111 \pm 0.008$ for CMASS and LOWZ, respectively, which is in agreement with the Planck $Λ$CDM best-fit $Ω_{\rm c}h^{2} n_{\rm s} = 0.116 \pm 0.001$.

astro-ph.CO↗

arXiv2021

Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions

We examine the relation between the Szekeres models and relativistic Lagrangian perturbation schemes, in particular the Relativistic Zel'dovich Approximation (RZA). We show that the second class of the Szekeres solutions is exactly contained within the RZA when the latter is restricted to an irrotational dust source with a flow-orthogonal foliation of spacetime. In such a case, the solution is governed by the first principal scalar invariant of the deformation field, proving a direct connection with a class of Newtonian three-dimensional solutions without symmetry. For the second class, a necessary and sufficient condition for the vanishing of cosmological backreaction on a scale of homogeneity is expressed through integral constraints. Domains with no backreaction can be smoothly matched, forming a lattice model, where exact deviations average out at a given scale of homogeneity, and the homogeneous and isotropic background is recovered as an average property of the model. Although the connection with the first class of Szekeres solutions is not straightforward, this class allows for the interpretation in terms of a spatial superposition of nonintersecting fluid lines, where each world line evolves independently and under the RZA model equations, but with different associated `local backgrounds'. This points to the possibility of generalizing the Lagrangian perturbation schemes to structure formation models on evolving backgrounds, including global cosmological backreaction.

gr-qc↗

arXiv2020

Gauss-Bonnet-Chern approach to the averaged Universe

The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark components open. Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity. The spatially averaged 3+1 Einstein equations are effective balance equations that need a closure condition. Heading for closure we here explore topological constraints. Results are straightforwardly obtained for averaged 2+1 model universes. For the relevant 3+1 case, we employ a method based on the Gauss-Bonnet-Chern theorem generalized to Lorentzian spacetimes and implement a sandwich approach to obtain spatial average properties. The 3+1 topological approach supplies us with a new equation linking evolution of scalar invariants of the expansion tensor to the norm of the Weyl tensor. From this we derive general evolution equations for averaged scalar curvature and kinematical backreaction, and we discuss related evolution equations on this level of the hierarchy of averaged equations. We also discuss the relation between topological properties of cosmological manifolds and dynamical topology change, e.g. as resulting from the formation of black holes.

gr-qc↗

arXiv2020

Solving the curvature and Hubble parameter inconsistencies through structure formation-induced curvature

Recently it has been noted by Di Valentino, Melchiorri and Silk (2019) that the enhanced lensing signal relative to that expected in the spatially flat $Λ$CDM model poses a possible crisis for the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) class of models usually used to interpret cosmological data. The 'crisis' amounts to inconsistencies between cosmological datasets arising when the FLRW curvature parameter $Ω_{k0}$ is determined from the data rather than constrained to be zero a priori. Moreover, the already substantial discrepancy between the Hubble parameter as determined by Planck and local observations increases to the level of $5σ$. While such inconsistencies might arise from systematic effects of astrophysical origin affecting the Planck Cosmic Microwave Background (CMB) power spectra at small angular scales, it is an option that the inconsistencies are due to the failure of the FLRW assumption. In this paper we recall how the FLRW curvature ansatz is expected to be violated for generic relativistic spacetimes. We explain how the FLRW conservation equation for volume-averaged spatial curvature is modified through structure formation, and we illustrate in a simple framework how the curvature tension in a FLRW spacetime can be resolved -- and is even expected to occur -- from the point of view of general relativity. Requiring early-time convergence towards a Friedmannian model with a spatial curvature parameter $Ω_{k0}$ equal to that preferred from the Planck power spectra resolves the Hubble tension within our dark energy-free model.

gr-qc↗

arXiv2020

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational dust models (Paper I) and irrotational perfect fluids (Paper II) in flow-orthogonal foliations of spacetime. It complements them by considering arbitrary foliations, arbitrary lapse and shift, and by allowing for a tilted fluid flow with vorticity. As for the first studies, the propagation of the spatial averaging domain is chosen to follow the congruence of the fluid, which avoids unphysical dependencies in the averaged system that is obtained. We present two different averaging schemes and corresponding systems of averaged evolution equations providing generalizations of Papers I and II. The first one retains the averaging operator used in several other generalizations found in the literature. We extensively discuss relations to these formalisms and pinpoint limitations, in particular regarding rest mass conservation on the averaging domain. The alternative averaging scheme that we subsequently introduce follows the spirit of Papers I and II and focuses on the fluid flow and the associated 1+3 threading congruence, used jointly with the 3+1 foliation that builds the surfaces of averaging. This results in compact averaged equations with a minimal number of cosmological backreaction terms. We highlight that this system becomes especially transparent when applied to a natural class of foliations which have constant fluid proper time slices.

gr-qc↗

arXiv2020

Editorial Note to: On the Newtonian Limit of Einstein's Theory of Gravitation (by Jürgen Ehlers)

We give an overview of literature related to Jürgen Ehlers' pioneering 1981 paper on Frame theory--a theoretical framework for the unification of General Relativity and the equations of classical Newtonian gravitation. This unification encompasses the convergence of one-parametric families of four-dimensional solutions of Einstein's equations of General Relativity to a solution of equations of a Newtonian theory if the inverse of a causality constant goes to zero. As such the corresponding light cones open up and become space-like hypersurfaces of constant absolute time on which Newtonian solutions are found as a limit of the Einsteinian ones. It is explained what it means to not consider the `standard-textbook' Newtonian theory of gravitation as a complete theory unlike Einstein's theory of gravitation. In fact, Ehlers' Frame theory brings to light a modern viewpoint in which the `standard' equations of a self-gravitating Newtonian fluid are Maxwell-type equations. The consequences of Frame theory are presented for Newtonian cosmological dust matter expressed via the spatially projected electric part of the Weyl tensor, and for the formulation of characteristic quasi-Newtonian initial data on the light cone of a Bondi-Sachs metric.

gr-qc↗