arXiv subjects

Marie-Noëlle Célérier

Publications and source records attributed to Marie-Noëlle Célérier.

At least 19 recordsLinked to original sources

arXiv2026

The cosmic multipoles: a consistency test for the Szekeres cosmological model

Some of the properties of the Szekeres solutions which have never been used in a cosmological context are known for long. In this letter, the total and unique decomposition of its matter energy density into a monopole and dipole moment is recalled and specialized to the axially symmetric quasi-spherical subclass of the model. All the model special features -- axial symmetry, spherical quasi-symmetry, location of the observer -- are observationally justified. Then, a consistency test of the model involving its no-high-multipole-in-mass-density property is proposed.

astro-ph.CO↗

arXiv2026

A ready-to-fit inhomogeneous cosmological model: The axially symmetric Szekeres spacetime

The purpose of the present work is based on two main observations: the tensions encountered by the standard $Λ$CDM model when confronted to precision small scale cosmological data and the finding that the matter distribution is dipolar and the expansion of the Universe is axially symmetric roughly in the direction of the CMB dipole. Therefore, we propose, as a model for the inhomogeneous local universe, an axially symmetric Szekeres solution. After describing its main properties, we are left with three metric functions to be fitted to data between the observer and the transition to homogeneity which is an intrinsic feature of Szekeres spacetimes. So as to turn a difficult functional inference problem into a classical parameter estimation problem, we propose to use Chebyshev polynomial expansions, which, as a first step, we truncate after the second order terms. We are thus left with nine constant parameters: six for the metric functions, plus the observer's location and the cosmological constant. Here are the proper ingredients needed to implement the data fitting to the model in the future.

astro-ph.CO↗

arXiv2026

Precision cosmology with exact inhomogeneous solutions of General Relativity: the Szekeres models

The exact Friedman solution to the field equations of General Relativity (GR) describing a homogeneous and isotropic universe together with its linear and higher-order perturbations are the theoretical roots of the current standard model of cosmology. However, despite its global successes, this standard model currently faces a number of tensions and anomalies, which occur mostly from a mismatch between early and late cosmic time region depictions. Actually, in the era of precision cosmology, the late inhomogeneities in the densities of the Universe components can no more be neglected. Moreover, since GR is fundamentally nonlinear, any linear perturbation theory is doomed to fail at reproducing precisely its features, while higher-order perturbed FLRW models cannot either claim the status of exact solution to Einstein's field equations. Fortunately, other GR solutions exist which are best suited for this purpose, e. g., exact inhomogeneous solutions able to represent a matter-cosmological constant dominated universe region. Among these, the Szekeres solution, which is devoid of any symmetry, appears as a proper tool for this purpose. Moreover, since these solutions possess the FLRW model as a homogeneous limit, they can be smoothly matched to the standard representation at the inhomogeneity-homogeneity transition. In this paper, the Szekeres solution and its main interesting properties, as well as the equations needed to use this solution in a cosmological context are presented. Then the prospects for a broader use of its abilities are sketched out. In particular, the use of neural networks is proposed to allow, in the future, the fitting of the huge amount of data becoming available to constrain the arbitrary functions and the constant parameters characterizing the Szekeres model, running for representing our late Universe with an increased precision.

gr-qc↗

arXiv2025

Gravitational collapse of anisotropic cylindrical shearfree fluids with new exact interior solutions of GR

We present a study of shearfree gravitational collapse using cylindrically symmetric spacetimes whose interior is a non-rotating dissipative fluid bounded by a cylindrical hypersurface beyond which is an Einstein-Rosen vacuum exterior. We consider three different pressure configurations: axially, azimuthally, and radially directed, for which we find new exact interior solutions of the field equations. We show that the matching conditions cannot be satisfied by the fluid with radial pressure, while the axial and azimuthal cases with a lapse function depending only on the time coordinate do satisfy these constraints. We derive, for both cases, a sufficient condition for an emission of gravitational radiation from the interior towards the exterior. Therefore we show that, at variance with what happens for spherical symmetry, in the simplified picture of an infinite cylinder of anisotropic shearfree matter, gravitational waves can be emitted during collapsing motion.

gr-qc↗

arXiv2024

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids: anisotropic pressure

In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid, followed by a fluid with an azimuthally directed pressure, and, finally, by a fluid where the pressure is radially oriented. The perfect fluid configuration has subsequently been extended to the case of differential rotation. In the present paper, three different cases of anisotropic pressure analogous to those studied for rigidly rotating motion are considered in turn for differentially rotating fluids. General methods for generating mathematical solutions to the field equations and physically well-behaved examples are displayed for the axial and azimuthal pressure cases. As regards radial pressure fluids, four classes of solutions naturally emerge from the corresponding Einstein's equations, among which one class, after being fully integrated, exhibits physically well-behaved solutions.

gr-qc↗

arXiv2023

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. Perfect fluids

In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D {\bf 104}, 064040 (2021); J. Math. Phys. {\bf 64}, 022501 (2023); J. Math. Phys. {\bf 64}, 032501 (2023); J. Math. Phys. {\bf 64}, 042501 (2023); and J. Math. Phys. {\bf 64}, 052502 (2023)]. This work is currently being extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering in turn the same three anisotropic pressure cases, as well as a perfect fluid source. Here, the perfect fluid case is considered, and different classes are identified as directly issuing from the field equations. Among them, an explicit analytical set of solutions is selected as displaying perfect fluid spacetimes. Its mathematical and physical properties are analyzed. Its matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed.

gr-qc↗

arXiv2023

Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. 3. Azimuthal pressure

An investigation of interior spacetimes sourced by stationary cylindrical anisotropic fluids is presented and specialized to rigidly rotating fluids with an azimuthally directed pressure. Based on the occurence of an extra degree of freedom in the equations, a general method for constructing different classes of exact solutions to the field equations has been found. Exemplifying such a recipe, a bunch of solutions are constructed. Axisymmetry and regularity conditions on the axis are examined and the spacetimes are properly matched to a vacuum exterior. A number of classes and subclasses are thus studied and an analysis of their features leads to sorting out two classes whose appropriate mathematical and physical properties are discussed. This work is part of a larger study of the influence of anisotropic pressure in GR, using cylindrical symmetry as a simplifying assumption, and considering in turn each principal stress direction. It has been initiated in companion Papers 1 and 2 where the pressure was assumed to be axially directed, and is followed by Paper 4 considering radial pressure and Paper 5 contrasting the previous results with analogous dust and perfect fluid solutions.

gr-qc↗

arXiv2023

Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids

In an important series of articles published during the 70's, Krasiński displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of perfect fluid. However, these solutions depend on an unspecified arbitrary function, which lead the author to claim that the equation of state of the fluid could not be obtained directly from the field equations but had to be added by hand. In the present article, we use a double ansatz which we have developed in 2021 and implemented at length into a series of recent papers displaying exact interior solutions for a stationary rotating cylindrically symmetric fluid with anisotropic pressure. This ansatz allows us to obtain here a fully integrated class of solutions to the Einstein equations, written with the use of very simple analytical functions, and to show that the equation of state of the fluid follows naturally from these field equations.

gr-qc↗

arXiv2021

New classes of exact interior nonvacuum solutions to the GR field equations for spacetimes sourced by a rigidly rotating stationary cylindrical anisotropic fluid

A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. These solutions are required to satisfy regularity and junction conditions so that they can be possibly used to represent rotating astrophysical objects. Mathematical and physical properties are analyzed. The spacetime two independent parameters are physically interpreted, and they are shown to define two different solution classes together with stating the latters' properties.

gr-qc↗

arXiv2020

Stationary cylindrical anisotropic fluid and new purely magnetic GR solutions

The properties of interior spacetimes sourced by stationary cylindrical anisotropic fluids are here analytically studied for both nonrigid and rigid rotation. As regards nonrigid rotation, this is, to our knowledge, the first work dedicated to such a study. We give here a complete equation set describing these spacetime properties. In particular, we focus our attention on both nonrigid and rigid rotation gravito-electromagnetic features and are thus led to display strong hints in favor of conjecturing purely electric Weyl tensor existence in this framework. We have also been able to characterize new purely magnetic physically consistent spacetimes and have found new rigidly rotating exact solution classes to the five Einstein's field equations pertaining to the issue and the two purely magnetic constraints we have derived for this purpose. This should be considered as a prominent result, since extremely few purely magnetic exact solutions are available in the literature.

gr-qc↗

arXiv2014

Emergence of complex and spinor wave functions in Scale Relativity. II. Lorentz invariance and bi-spinors

Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity field of geodesics of a continuous and non-differentiable (therefore fractal) space-time. In a first paper (Paper I), we have presented the general argument which leads to this result using an elaborate and more detailed derivation than previously displayed. We have therefore been able to show how the complex wave function emerges naturally from the doubling of the velocity field and to revisit the derivation of the non relativistic Schrödinger equation of motion. In the present paper (Paper II) we deal with relativistic motion and detail the natural emergence of the bi-spinors from such first principles of the theory. Moreover, while Lorentz invariance has been up to now inferred from mathematical results obtained in stochastic mechanics, we display here a new and detailed derivation of the way one can obtain a Lorentz invariant expression for the expectation value of the product of two independent fractal fluctuation fields in the sole framework of the theory of Scale Relativity. These new results allow us to enhance the robustness of our derivation of the two main equations of motion of relativistic quantum mechanics (the Klein-Gordon and Dirac equations) which we revisit here at length.

physics.gen-ph↗

arXiv2014

Redshift and redshift-drift in $Λ= 0$ quasi-spherical Szekeres cosmological models and the effect of averaging

Since the advent of the accelerated expanding homogeneous universe model, some other explanations for the supernova Ia dimming have been explored, among which there are inhomogeneous models constructed with exact $Λ= 0$ solutions of Einstein's equations. They have been used either as one patch or to build Swiss-cheese models. The most studied ones have been the Lemaître-Tolman-Bondi (LTB) models. However, these models being spatially spherical, they are not well designed to reproduce the large scale structures which exhibit clusters, filaments and non spherical voids. This is the reason why Szekeres models, which are devoid of any symmetry, have recently come into play. In this paper, we give the equations and an algorithm to compute the redshift-drift for the most general quasi-spherical Szekeres (QSS) models with no dark energy. We apply it to a QSS model recently proposed by Bolejko and Sussman (BSQSS model) who averaged their model to reproduce the density distribution of the Alexander and collaborators' LTB model which is able to fit a large set of cosmological data without dark energy. They concluded that their model represents a significant improvement over the observed cosmic structure description by spherical LTB models. We show here that this QSS model is ruled out by a negative cosmological redshift, i.e. a blueshift, which is not observed in the Universe. We also compute a positive redshift and the redshift-drift for the Alexander et al.'s model and compare this redshift-drift to that of the $Λ$CDM model. We conclude that the process of averaging an unphysical QSS model can lead to obtain a physical model able to reproduce our observed local Universe with no dark energy need and that the redshift-drift can discriminate between this model and the $Λ$CDM model. For completeness, we also compute the blueshift-drift of the BSQSS model.

astro-ph.CO↗

arXiv2013

Emergence of complex and spinor wave functions in scale relativity. I. Nature of scale variables

One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owing to the scale-dependence which it induces, non-differentiability involves a fundamental two-valuedness of the mean derivatives. Since, in the scale relativity framework, the wave function is a manifestation of the velocity field of fractal space-time geodesics, the two-valuedness of velocities leads to write them in terms of complex numbers, and yields therefore the complex nature of the wave function, from which the usual expression of the Schrödinger equation can be derived.

physics.gen-ph↗

arXiv2013

Redshift-drift as a test for discriminating between decelerating inhomogeneous and accelerating universe models

Exact inhomogeneous solutions of Einstein's equations have been used in the literature to build models reproducing the cosmological data without dark energy. However, owing to the degrees of freedom pertaining to these models, it is necessary to get rid of the degeneracy often exhibited by the problem of distinguishing between them and accelerating universe models. We give an overview of redshift drift in inhomogeneous cosmologies, and explain how it serves to this purpose. One class of models which fits the data is the Szekeres Swiss-cheese class where non-spherically symmetric voids exhibit a typical size of about 400 Mpc. We present our calculation of the redshift drift in this model, and compare it with the results obtained by other authors for alternate scenarios.

astro-ph.CO↗

arXiv2012

Fully Characterizing Axially Symmetric Szekeres Models With Three Data Sets

Inhomogeneous exact solutions of General Relativity with zero cosmological constant have been used in the literature to challenge the ΛCDM model. From one patch Lemaître-Tolman-Bondi (LTB) models to axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese models, some of them are able to reproduce to a good accuracy the cosmological data. It has been shown in the literature that a zero-Λ-LTB model with a central observer can be fully determined by two data sets. We demonstrate that an axially symmetric zero-Λ-QSS model with an observer located at the origin can be fully reconstructed from three data sets, number counts, luminosity distance and redshift drift. This is a first step towards a future demonstration involving five data sets and the most general Szekeres model.

gr-qc↗

arXiv2012

Redshift drift in axially symmetric quasi-spherical Szekeres models

Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss-cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae (SNIa). However, the problem of fitting such models to the SNIa data is completely degenerate and we need other constraints to fully characterize them. One of the tests which is known to be able to discriminate between different cosmological models is the redshift-drift. This drift has already been calculated by different authors for Lemaître-Tolman-Bondi (LTB) models. We compute it here for one particular axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which has previously been shown to reproduce to a good accuracy the SNIa data, and we compare the results to the drift in the $Λ$CDM model and in some LTB models that can be found in the literature. We show that it is a good discriminator between them. Then, we discuss our model's remaining degrees of freedom and propose a recipe to fully constrain them.

astro-ph.CO↗

arXiv2012

Some clarifications about Lemaître-Tolman models of the Universe used to deal with the dark energy problem

During the past fifteen years, inhomogeneous cosmological models have been put forward to explain the observed dimming of the SNIa luminosity without resorting to dark energy. The simplest models are the spherically symmetric Lemaître-Tolman (LT) solutions with a central observer. Their use must be considered as a mere first step towards more sophisticated models. Spherical symmetry is but a mathematical simplification and one must consider spherical symmetric models as exhibiting an energy density smoothed out over angles around us. However, they have been taken at face value by some authors who tried to use them for either irrelevant purposes or to put them to the test as if they were robust models of our Universe. We wish to clarify how these models must be used in cosmology. We first use the results obtained by Iguchi and collaborators to derive the density profiles of the pure growing and decaying mode LT models. We then discuss the relevance of the different test proposals in the light of the interpretation given above. We show that decaying-mode (parabolic) LT models always exhibit an overdensity near their centre and growing-mode (elliptic or hyperbolic) LT models, a void. This is at variance with some statements in the literature. We dismiss all previous proposals merely designed to test the spherical symmetry of the LT models, and we agree that the value of $H_0$ and the measurement of the redshift drift are valid tests of the models. However, we suspect that this last test, which is the best in principle, will be more complicated to implement than usually claimed.

astro-ph.CO↗

arXiv2012

Effects of inhomogeneities on the expansion of the Universe: a challenge to dark energy?

The current standard model of cosmology, the LambdaCDM model, is based on the homogeneous FLRW solutions of the Einstein equations to which some perturbations are added to account for the CMB features and structure formation at large scales. This model fits rather well the observations provided 95% of the energy density budget of the Universe should be of an unknown physical nature, i.e. dark matter and dark energy. Now, the aim of a cosmological model is not merely to reproduce the observations, but also to give a physical understanding of the Universe we live in. Moreover, even if the assumption of homogeneity seems to be more or less valid at large scales, it appears to be in contradiction with observations at intermediate scales (between the scale of non linear structure formation and that where structures virialize). This is the reason why, during the last decade, a community of researchers formed whose aim was to look for the best way to take into account the influence of the inhomogeneities seen in the Universe and to construct accurate cosmological models which could possibly get rid of the dark components. This task, which is still in its infancy, is currently progressing towards promising results. Two types of methods can be found in the literature: spatial averaging of scalar quantities and use of exact inhomogeneous solutions of General Relativity. We will give here a brief report of the second one.

astro-ph.CO↗