arXiv subjects

Marie-Noëlle Célérier

Publications and source records attributed to Marie-Noëlle Célérier.

At least 37 records · Page 2Linked to original sources

arXiv2011

Inhomogeneous cosmological models: exact solutions and their applications

Recently, inhomogeneous generalisations of the Friedmann-Lemaitre-Robertson-Walker cosmological models have gained interest in the astrophysical community and are more often employed to study cosmological phenomena. However, in many papers the inhomogeneous cosmological models are treated as an alternative to the FLRW models. In fact, they are not an alternative, but an exact perturbation of the latter, and are gradually becoming a necessity in modern cosmology. The assumption of homogeneity is just a first approximation introduced to simplify equations. So far this assumption is commonly believed to have worked well, but future and more precise observations will not be properly analysed unless inhomogeneities are taken into account. This paper reviews recent developments in the field and shows the importance of an inhomogeneous framework in the analysis of cosmological observations.

astro-ph.CO↗

arXiv2011

Szekeres Swiss-Cheese model and supernova observations

We use different particular classes of axially symmetric Szekeres Swiss-cheese models for the study of the apparent dimming of the supernovae of type Ia. We compare the results with those obtained in the corresponding Lemaitre-Tolman Swiss-cheese models. Although the quantitative picture is different the qualitative results are comparable, i.e, one cannot fully explain the dimming of the supernovae using small scale ~50 Mpc inhomogeneities. To fit successfully the data we need structures of order of 500 Mpc size or larger. However, this result might be an artifact due to the use of axial light rays in axially symmetric models. Anyhow, this work is a first step in trying to use Szekeres Swiss-cheese models in cosmology and it will be followed by the study of more physical models with still less symmetry.

astro-ph.CO↗

arXiv2010

Electromagnetic Klein-Gordon and Dirac equations in scale relativity

We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scale-covariant derivative tool. Finally, the electromagnetic Klein-Gordon equation has been recovered with a covariant derivative constructed by combining the quantum-covariant velocity operator and the scale-covariant derivative. We show here that if one tries to derive the electromagnetic Dirac equation from the Klein-Gordon one as for the free particle motion, i.e. as a square root of the time part of the Klein-Gordon operator, one obtains an additional term which is the relativistic analog of the spin-magnetic field coupling term of the Pauli equation. However, if one first applies the quantum covariance, then implements the scale covariance through the scale-covariant derivative, one obtains the electromagnetic Dirac equation in its usual form. This method can also be applied successfully to the derivation of the electromagnetic Klein-Gordon equation. This suggests it rests on more profound roots of the theory, since it encompasses naturally the spin-charge coupling.

physics.gen-ph↗

arXiv2010

A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model

Lemaître - Tolman (L--T) toy models with a central observer have been used to study the effect of large scale inhomogeneities on the SN Ia dimming. Claims that a giant void is mandatory to explain away dark energy in this framework are currently dominating. Our aim is to show that L-T models exist that reproduce a few features of the $Λ$CDM model, but do not contain the giant cosmic void. We propose to use two sets of data - the angular diameter distance together with the redshift-space mass-density and the angular diameter distance together with the expansion rate - both defined on the past null cone as functions of the redshift. We assume that these functions are of the same form as in the $Λ$CDM model. Using the Mustapha-Hellaby-Ellis algorithm, we numerically transform these initial data into the usual two L-T arbitrary functions and solve the evolution equation to calculate the mass distribution in spacetime. For both models, we find that the current density profile does not exhibit a giant void, but rather a giant hump. However, this hump is not directly observable, since it is in a spacelike relation to a present observer. The alleged existence of the giant void was a consequence of the L-T models used earlier because their generality was limited a priori by needless simplifying assumptions, like, for example, the bang-time function being constant. Instead, one can feed any mass distribution or expansion rate history on the past light cone as initial data to the L-T evolution equation. When a fully general L-T metric is used, the giant void is not implied.

astro-ph.CO↗

arXiv2009

Chaotic motion in classical fluids with scale relativistic methods

In the framework of the scale relativity theory, the chaotic behavior in time only of a number of macroscopic systems corresponds to motion in a space with geodesics of fractal dimension 2 and leads to its representation by a Schrödinger-like equation acting in the macroscopic domain. The fluid interpretation of such a Schrödinger equation yields Euler and Navier-Stokes equations. We therefore choose to extend this formalism to study the properties of a system exhibiting a chaotic behavior both in space and time which amounts to consider them as issued from the geodesic features of a mathematical object exhibiting all the properties of a fractal `space-time'. Starting with the simplest Klein-Gordon-like form that can be given to the geodesic equation in this case, we obtain a motion equation for a `three fluid' velocity field and three continuity equations, together with parametric expressions for the three velocity components which allow us to derive relations between their non-vanishing curls. At the non relativistic limit and owing to the physical properties exhibited by this solution, we suggest that it could represent some kind of three-dimensional chaotic behavior in a classical fluid, tentatively turbulent if particular conditions are fulfilled. The appearance of a transition parameter ${\cal D}$ in the equations allows us to consider different ways of testing experimentally our proposal.

physics.flu-dyn↗

arXiv2009

Motion equations for relativistic particles in an external electromagnetic field in scale relativity

Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon equation by taking its square root in a bi-quaternionic formalism fully justified by the first principles of the scale relativity theory. This is no more true when an external electro-magnetic field comes into play. If one tries to derive the electro-magnetic Dirac equation in a manner analogous to the one used when this field is absent, one obtains an additional term which is the relativistic analogue of the spin-magnetic field coupling term encountered in the Pauli equation, valid for a non-relativistic particle with spin 1/2. There is however a method to recover the standard form of the electro-magnetic Dirac equation, with no additional term, which amounts modifying the way both covariances involved here, quantum and scale, are implemented. Without going into technical details, it will be shown how these results suggest this last method is based on more profound roots of the scale relativity theory since it encompasses naturally the spin-charge coupling.

physics.gen-ph↗

arXiv2009

Study of chaotic motion in fluid mechanics with the scale relativity methods

Chaotic motion in time of a number of macroscopic systems has been analyzed, in the framework of scale relativity, as motion in a fractal space with topological dimension 3 and geodesics with fractal dimension 2. The motion equation is then Schrödinger-like and its interpretation in fluid mechanics gives the well-known Euler and Navier-Stokes equations. We generalize here this formalism to the study of a system exhibiting a chaotic behavior both in space and time. We are thus lead to consider macroscopic fluid properties as issuing from the geodesic features of a fractal `space-time' with topological dimension 4 and geodesics with fractal dimension 2. This allows us to obtain both a motion equation for the fluid velocity field, which exhibits then three components while only one is necessary for the description of an ordinary fluid, and a relation between their three curls. The physical properties of this solution suggest it could represent some three-dimensional chaotic behavior for a classical fluid, tentatively turbulent if particular conditions are fulfilled. Different ways of testing experimentally these assumptions are proposed.

physics.gen-ph↗

arXiv2009

Inhomogeneities in the Universe with exact solutions of General Relativity

It is commonly stated that we have entered the era of precision cosmology in which a number of important observations have reached a degree of precision, and a level of agreement with theory, that is comparable with many Earth-based physics experiments. One of the consequences is the need to examine at what point our usual, well-worn assumption of homogeneity associated to the use of perturbation theory begins to compromise the accuracy of our models. It is now a widely accepted fact that the effect of the inhomogeneities observed in the Universe cannot be ignored when one wants to construct an accurate cosmological model. Well-established physics can explain several of the observed phenomena without introducing highly speculative elements, like dark matter, dark energy, exponential expansion at densities never attained in any experiment (i.e. inflation), and the like. Two main classes of methods are currently used to deal with these issues. Averaging, sometimes linked to fitting procedures a la Stoegger and Ellis, provide us with one promising way of solving the problem. Another approach is the use of exact inhomogeneous solutions of General Relativity. This will be developed here.

physics.gen-ph↗

arXiv2008

Scaling Regimes as obtained from the DR5 Sloan Digital Sky Survey

Standard cosmology is based on the assumption that the universe is spatially homogeneous. However the consensus on a homogeneous matter structure, even on very large scales, has never been complete. The advantage of correlation dimension calculations is that they enable one to obtain the transition scale to a homogeneous distribution, whereas other methods, such as those using the two-point correlation function, make it hard to exhibit the possible fractal properties of the Universe matter content. Our purpose is to calculate the correlation dimension $D_2$, looking for a possible transition to homogeneity, which would imply $D_2 = 3$. We apply the correlation integral method to the three dimensional sample composed of 332,876 galaxies which we extract from the Fifth Data Release of the Sloan Digital Sky Survey. We analyze the raw data up to the scale $d_{max} = 160$ Mpc, assuming $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$ and considering three cosmological models in order to test the model dependence of our method. Using volume limited samples for this range leaves us with about 20,000 galaxies. Applying our method to random maps helps us to calibrate our results. We obtain a correlation dimension of the galaxy distribution which seems to increase with scales up to $D_2=3$ reached around 70 Mpc. The results of our analysis, performed on the largest volume limited sample which can be extracted from the SDSS catalog, are compatible with those formerly obtained by other authors. However, to get a more reliable description of the structures at various scales, we think it will be mandatory to use still larger catalogs than those which are currently available.

astro-ph↗

arXiv2007

Derivation of the postulates of quantum mechanics from the first principles of scale relativity

Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in the framework of the theory of scale relativity. After having analyzed the actual status of the various postulates, rules and principles that underlie the present axiomatic foundation of quantum mechanics (in terms of main postulates, secondary rules and derived `principles'), we attempt to provide the reader with an exhaustive view of the matter, by both gathering here results which are already available in the literature, and deriving new ones which complete the postulate list.

quant-ph↗

arXiv2007

Do we really see a cosmological constant in the supernovae data ?

The magnitude-redshift relation is one of the tools for a direct observational approach to cosmology. The discovery of high redshift Type Ia supernovae (SNIa) and their use as ``standard candles'' has resurrected interest in this approach. Recently collected data have been used to address the problem of measuring the cosmological parameters of the universe. Analysed in the framework of homogeneous models, they have yielded, as a primary result, a strictly positive cosmological constant. However, a straight reading of the published measurements, conducted with no a priori idea of which model would best describe our universe at least up to redshifts $z\sim 1$, does not exclude the possibility of ruling out the Cosmological Principle - and cosmological constant - hypotheses. It is therefore shown here how the large scale homogeneity of this part of the universe can be tested on our past light cone, using the magnitude-redshift relation, provided sufficiently accurate data from sources at redshifts approaching $z=1$ would be available. An exemple of an inhomogeneous model with zero cosmological constant reproducing the current observations is given. The presently published SNIa data can thus be interpreted as implying either a strictly positive cosmological constant in a homogeneous universe or large scale inhomogeneity with no constraint on $Λ$. An increase in the number and measurement accuracy of the candidate ``standard candles'' at very high redshift is therefore urgently needed, for progress in both fundamental issues of the Cosmological Principle and cosmological constant.

astro-ph↗

arXiv2007

Inhomogeneities in the Universe and the Fitting Problem

Observational cosmology provides us with a large number of high precision data which are used to derive models trying to reproduce ``on the mean'' our observable patch of the Universe. Most of these attempts are achieved in the framework of a Friedmann-Lemaître cosmology where large scale homogeneity is assumed. However, we know, from the observation of structures at increasing scales, that these models are only approximations of a smoothed or averaged inhomogeneous underlying patern. Anyhow, when modelling the Universe, the usual method is to use continuous functions representing the kinematical scalars of the velocity field, implicitly assuming that they represent volume averages of the corresponding fine-scale inhomogeneous quantities, then put them into the Einstein equations which are solved to give the model and its dependance upon a number of parameters arbitrarily defined. In General Relativity, such a method is very much involved since the equations which determine the metric tensor and the quantities calculated from it are highly nonlinear. The question raised by the method consisting of determining the parameters of an a priori assumed FLRW model from observational data is the ``fitting problem'' brought to general attention by Ellis and Stoeger in the 80's. This problem has recently experienced a reniewed attention due to the amount of available data and the increase of the minimum scale at which homogeneity can be assumed. We propose a discussion of this issue in the light of the latest developments of observational and theoretical cosmology.

astro-ph↗

arXiv2007

The Accelerated Expansion of the Universe Challenged by an Effect of the Inhomogeneities. A Review

Since its decovery during the late 90's, the dimming of distant SN Ia apparent luminosity has been mostly ascribed to the influence of a mysterious dark energy component. Formulated in a Friedmannian cosmological modelling framework based upon the cosmological ``principle'' hypothesis, this interpretation has given rise to the ``concordance'' model. However, a caveat of such a reasoning is that the cosmological ``principle'' derives from a philosophical Copernican assumption and has never been tested. Furthermore, a weakness of its conclusion, i. e., the existence of a negative-pressure fluid or a cosmological constant, is that it would have profound implications for the current theories of physics. This is why we have proposed a more conservative explanation, ascribing the departure of the observed universe from an Einstein-de Sitter model to the influence of inhomogeneities. This idea has been independently developed by other authors and further enlarged to the reproduction of different cosmological data. We review here the main proposals which have been put forward to deal with this purpose and present some prospects for future developments.

astro-ph↗

arXiv2006

Is the apparent acceleration of the Universe expansion driven by a dark energy-like component or by inhomogeneities?

Since its decovery during the late 90's, the dimming of distant SN Ia apparent luminosity has been mostly ascribed to the influence of a mysterious dark energy component. Based upon the cosmological "principle" hypothesis, this interpretation has given rise to the "concordance" model, developed in the context of a Friedmann-Lemaitre cosmology. However, a caveat of this reasoning is that the cosmological "principle" derives from a philosophical Copernican assumption and has never been tested. Furthermore, a weakness of its conclusion, i. e., the existence of a negative-pressure fluid or a cosmological constant, is that it would have profound implications for the current theories of physics. This is why we have proposed a more conservative explanation, ascribing the departure of the observed universe from an Einstein-de Sitter model to the influence of inhomogeneities. This idea has been independently developed by other authors and further enlarged to the reproduction of different cosmological data. We review here the main proposals which has been made along these lines of though and present some prospects for future developments.

astro-ph↗

arXiv2006

Quantum-classical transition in Scale Relativity

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The Schrodinger and Klein-Gordon equations are demonstrated as geodesic equations in this framework. A development of the intrinsic properties of this theory, using the mathematical tool of Hamilton's bi-quaternions, leads us to a derivation of the Dirac equation within the scale-relativity paradigm. The complex form of the wavefunction in the Schrodinger and Klein-Gordon equations follows from the non-differentiability of the geometry, since it involves a breaking of the invariance under the reflection symmetry on the (proper) time differential element (ds <-> - ds). This mechanism is generalized for obtaining the bi-quaternionic nature of the Dirac spinor by adding a further symmetry breaking due to non-differentiability, namely the differential coordinate reflection symmetry (dx^mu <-> - dx^mu) and by requiring invariance under parity and time inversion. The Pauli equation is recovered as a non-relativistic-motion approximation of the Dirac equation.

quant-ph↗

arXiv2006

Non-Abelian gauge field theory in scale relativity

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ``scale-space''. We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.

hep-th↗

arXiv2000

Relativistic corrections to fractal analyses of the galaxy distribution

The effect of curvature on the results of fractal analyses of the galaxy distribution is investigated. We show that, if the universe satisfies the criteria of a wide class of parabolic homogeneous models, the observers measuring the fractal index with the integrated conditional density procedure may use the Hubble formula, without having to allow for curvature, out to distances of 600 Mpc, and possibly far beyond. This contradicts a previous claim by Ribeiro (1995) that, in the Einstein-de Sitter case, relativistic corrections should be taken into account at much smaller scales. We state for the class of cosmological models under study, and give grounds for conjecture for others, that the averaging procedure has a smoothing effect and that, therefore, the redshift-distance relation provides an upper limit to the relativistic corrections involved in such analyses.

astro-ph↗

arXiv2000

Models of Universe with a Delayed Big-Bang singularity. III. Solving the horizon problem for an off-center observer

This paper is the third of a series dedicated to the study of the Delayed Big-Bang (DBB) class of inhomogeneous cosmological models of Lemaître-Tolman-Bondi type. In the first work, it was shown that the geometrical properties of the DBB model are such that the horizon problem can be solved, without need for any inflationary phase, for an observer situated sufficiently near the symmetry center of the model to justify the ``centered earth'' approximation. In the second work, we studied, in a peculiar subclass of the DBB models, the extent to which the values of the dipole and quadrupole moments measured in the cosmic microwave background radiation (CMBR) temperature anisotropies can support a cosmological origin. This implies a relation between the location of the observer in the universe and the model parameter value: the farther the observer from the symmetry center, the closer our current universe to a local homogeneous pattern. However, in this case, the centered earth approximation is no longer valid and the results of the first work do not apply. We show here that the horizon problem can be solved, in the DBB model, also for an off-center observer, which improves the consistency of this model regarding the assumption of a CMBR large scale anisotropy cosmological origin.

gr-qc↗