arXiv subjects

Jan J. Ostrowski

Publications and source records attributed to Jan J. Ostrowski.

At least 19 recordsLinked to original sources

arXiv2025

Relativistic models of structure formation with stable end-state configuration

The aim of this paper is to provide an analytical model for the formation of stable structures (cosmological or astrophysical), where stability is obtained through the tangential pressure countering the effect of gravity. We utilize the generalization of the Lemaitre-Tolman-Bondi (LTB) spacetime to matter with tangential pressure generated by the angular momentum of fluid particles. Extending the Krasiński-Hellaby (KH) LTB reconstruction method, we show how set of three functions defined on two arbitrary hypersurfaces can fully determine the spacetime geometry. We further restrict our attention to the bounded case and develop the weak-field and the small-angular-momentum approximations. We show how these can be applied to the exact solution on the initial hypersurface, together with the oscillatory solution on the final hypersurface, to considerably simplify the reconstruction scheme. The so obtained models exhibit explicit dust-like behaviour in the early and middle stages of the collapse, and reach the final state as oscillations around the static solution.

gr-qc↗

arXiv2024

Average zero-expansion regions of the universe

Persistent tensions in the $Λ$CDM cosmological model underline the importance of tests of its basic assumptions. One such potential test arises from the fact that the surface of zero expansion around the collapsing object with spherical symmetry is strictly related to the object's mass and the value of the cosmological constant. We propose a complementary probe relating the averaged zero-expansion volume to the mass and the background cosmological Hubble parameter. Using the relativistic Zel'dovich approximation we are able to relax the spherical symmetry assumption and hence obtain a more general test of cosmological dynamics. Alternatively, our method can serve as a test of compatibility of relativistic N-body simulations and the scalar, averaged Einstein's equations with the relativistic Zel'dovich approximation serving as a closure condition.

astro-ph.CO↗

arXiv2024

The model of the local Universe in the framework of the second-order perturbation theory

Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann-Lemaitre-Robertson-Walker (FLRW) background filled with dust matter and a positive cosmological constant. In this paper, we use the Cosmicflows-4 (CF4) sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lemaitre-Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

astro-ph.CO↗

arXiv2024

Relativistic modeling of cosmological structures with Bianchi IX spacetimes

We develop a relativistic framework to investigate the evolution of cosmological structures from the initial density perturbations to the highly nonlinear regime. Our approach involves proposing a procedure to match ``best-fit", exact Bianchi IX (BIX) spacetimes to finite regions within the perturbed Friedmann-Lemaitre-Robertson-Walker universe characterized by a positive averaged spatial curvature. This method enables us to approximately track the nonlinear evolution of the initial perturbation using an exact solution. Unlike standard perturbation theory and exact solutions with a high degree of symmetry (such as spherical symmetry), our approach is applicable to generic initial data, with the only requirement being positive spatial curvature. By employing the BIX symmetries, we can systematically incorporate the approximate effects of shear and curvature into the process of collapse. Our approach addresses the limitations of both standard perturbation theory and highly symmetric exact solutions, providing valuable insights into the nonlinear evolution of cosmological structures.

gr-qc↗

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.

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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.

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arXiv2021

On the maximum volume of collapsing structures

In many cosmological models, including the $Λ$CDM concordance model, there exist a theoretical upper bounds on the size of collapsing structures. The most common formulations in the literature refer to a turnaround radius in spherical symmetry or a turnaround surface, defined as the zero-expansion boundary separating the outer Hubble flow from the inner flow of a collapsing fluid. In order to access a generic scenario, we propose an improvement of this cosmological test in terms of the maximum volume of the cosmological structures, which is equivalent to a zero-averaged expansion -- instead of the zero-local expansion. By combining the Lagrangian perturbations method and the scalar averaging of Einstein's equations, we obtain a maximum volume for a collapse model without any restricting symmetries. We compare this result with some exact, inhomogeneous solutions and discuss further potential developments.

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arXiv2019

A few numbers from the turnaround epoch of collapse

The turnaround epoch of gravitational collapse is examined by means of relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid's evolution reveal some scale-independent universality of parameters for a wide variety of initial conditions. In particular, the density contrast of the collapsing domain at the turnaround is shown to be significantly smaller than the value provided by Eulerian perturbative (homogeneous and spherical) model. Combined curvature and kinematical backreaction are shown to be of the order of the energy density. Possible improvements of our treatment are put into perspective.

gr-qc↗

arXiv2019

Does spatial flatness forbid the turnaround epoch of collapsing structures?

Cosmological observational analysis frequently assumes that the Universe is spatially flat. We aim to non-perturbatively check the conditions under which a flat or nearly flat expanding dust universe, including the LCDM model if interpreted as strictly flat, forbids the gravitational collapse of structure. We quantify spatial curvature at turnaround. We use the Hamiltonian constraint to determine the pointwise conditions required for an overdensity to reach its turnaround epoch in an exactly flat spatial domain. We illustrate this with a plane-symmetric, exact, cosmological solution of the Einstein equation, extending earlier work. More generally, for a standard initial power spectrum, we use the relativistic Zel'dovich approximation implemented in 'inhomog' to numerically estimate how much positive spatial curvature is required for turnaround to be allowed at typical epochs/length scales in almost-EdS and almost-LCDM models with inhomogeneous curvature. We find that gravitational collapse in a spatially exactly flat, irrotational, expanding, dust universe is relativistically forbidden pointwise. In the spatially flat plane-symmetric model considered here, pancake collapse is excluded both pointwise and in averaged domains. In an almost-EdS or LCDM model, the per-domain average curvature in collapsing domains almost always becomes strongly positive prior to turnaround, with the expansion-normalised curvature functional reaching $Ω_{\cal R}^{\cal D} \sim -5$. We show analytically that a special case gives $Ω_{\cal R}^{\cal D} = -5$ exactly (if normalised using the EdS expansion rate) at turnaround. An interpretation of LCDM as literally 3-Ricci flat would forbid structure formation. The difference between relativistic cosmology and a strictly flat LCDM model is fundamental in principle, but we find that the geometrical effect is weak.

astro-ph.CO↗

arXiv2018

The environment-dependence of the growth of the most massive objects in the Universe

This paper investigates the growth of the most massive cosmological objects. We utilize the Simsilun simulation, which is based on the approximation of the silent universe. In the limit of spatial homogeneity and isotropy the silent universes reduce to the standard FLRW models. We show that within the approximation of the silent universe the formation of the most massive cosmological objects differs from the standard background-dependent approaches. For objects with masses above $10^{15} M_\odot$ the effect of spatial curvature (overdense regions are characterized by positive spatial curvature) leads to measurable effects. The effect is analogous to the effect that the background cosmological model has on the formation of these objects (i.e. the higher matter density and spatial curvature the faster the growth of cosmic structures). We measure this by the means of the mass function and show that the mass function obtained from the Simsilun simulation has a higher amplitude at the high-mass end compared to standard mass function such as the Press-Schechter or the Tinker mass function. For comparison, we find that the expected mass of most massive objects using the Tinker mass function is $4.4^{+0.8}_{-0.6} \, \times 10^{15} M_\odot$, whereas for the Simsilun simulation is $6.3^{+1.0}_{-0.8} \, \times 10^{15} M_\odot$. We conclude that the nonlinear relativistic effects could affect the formation of the most massive cosmological objects, leading to a relativistic environment-dependence of the growth rate of the most massive clusters.

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

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↗

arXiv2015

On the Green and Wald formalism

Backreaction in the cosmological context is a longstanding problem that is especially important in the present era of precise cosmology. The standard model of a homogeneous background plus density perturbations is most probably oversimplified and is expected to fail to fully account for the near-future observations of sub-percent precision. From a theoretical point of view, the problem of backreaction is very complicated and deserves careful examination. Recently, Green and Wald claimed in a series of papers to have developed a formalism to properly describe the influence of density inhomogeneities on average properties of the Universe, i.e., the backreaction effect. A brief discussion of this framework is presented, focussing on its drawbacks and on misconceptions that have arisen during the "backreaction debate".

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↗

arXiv2015

Evidence for an environment-dependent shift in the baryon acoustic oscillation peak

The Friedmann-Lemaitre-Robertson-Walker (FLRW) metric assumes comoving spatial rigidity of metrical properties. The curvature term in comoving coordinates is environment-independent and cannot evolve. In the standard model, structure formation is interpreted accordingly: structures average out on the chosen metrical background, which remains rigid in comoving coordinates despite nonlinear structure growth. The latter claim needs to be tested, since it is a hypothesis that is not derived using general relativity. We introduce a test of the comoving rigidity assumption by measuring the two-point auto-correlation function on comoving scales---assuming FLRW comoving spatial rigidity---in order to detect shifts in the baryon acoustic oscillation (BAO) peak location for Large Red Galaxy (LRG) pairs of the Sloan Digital Sky Survey Data Release 7. In tangential directions, subsets of pairs overlapping with superclusters or voids show the BAO peak. The tangential BAO peak location for overlap with Nadathur & Hotchkiss superclusters is $4.3\pm1.6$ Mpc/h less than that for LRG pairs unselected for supercluster overlap, and $6.6\pm2.8$ Mpc/h less than that of the complementary pairs. Liivamagi et al. superclusters give corresponding differences of $3.7\pm2.9$ Mpc/h and $6.3\pm2.6$ Mpc/h, respectively. We have found moderately significant evidence (Kolmogorov--Smirnov tests suggest very significant evidence) that the BAO peak location for supercluster-overlapping pairs is compressed by about 6% compared to that of the complementary sample, providing a potential challenge to FLRW models and a benchmark for predictions from models based on an averaging approach that leaves the spatial metric a priori unspecified.

astro-ph.CO↗

arXiv2013

Virialization-induced curvature versus dark energy

The concordance model is successful in explaining numerous observable phenomena at the price of introducing an exotic source of unknown origin: dark energy. Dark energy dominance occurs at recent epochs, when we expect most cosmological structures to have already formed, and thus, when the error induced by forcing the homogeneous FLRW metric onto the data is expected to be the most significant. We propose a way to quantify the impact of deviations from homogeneity on the evolution of cosmological parameters. Using a multi-scale partitioning approach and the virialization fraction estimated from numerical simulations in an Einstein-de Sitter model, we obtain an observationally realistic distance modulus over redshifts 0 < z < 3 by a relativistic correction of the FLRW metric.

astro-ph.CO↗