08.09.2017 /
Jan. J. Ostrowski (Postdoc LIO, CRAL) :
Cosmological backreaction conjecture:
recent developments and future prospects
Inhomogeneous, relativistic cosmology has recently observed a rise in popularity among
the scientific community. In particular, the scalar averaging approach has been intensively
examined both analytically and numerically, giving some new insights into the problem of
cosmological backreaction, i.e. the conjectured influence of small scale density
inhomogeneities on the large scale evolution of the Universe. In my talk, I will summarize
these recent efforts including the Green and Wald theorem and several results from N-body
simulations, and I present future prospects of cosmological backreaction investigations.
10-12.10.2017 /
Thomas Buchert (ERC PI, CRAL) :
Doctoral School : Inhomogeneous Cosmology and the Dark Universe (Université and Observatoire de Strasbourg)
The standard cosmological model is a successful fitting model to observational data. It leaves, however, in suspense an explanation of the physical origin of Dark Energy and Dark Matter. The contribution of the former converges to about 68 percent and that for the latter to about 27 percent of the sources of the standard cosmological equations, up to a few percent that have to be attributed to known sources such as baryonic matter, radiation and neutrinos.
There exist a large number of international projects that deal with the Dark Energy problem of standard cosmology. However, most of the efforts focus on (i) alternative theories of gravitation, or (ii) the study of phenomenological models for postulated new fundamental fields. Other large experiments are conducted worldwide to search for Dark Matter. Here again the solution of the Dark Matter problem is seen (i) either in the modification of the laws of gravitation, or (ii) in postulating the existence of new fundamental fields, therefore challenging current theories of particle physics. These broad lines of research are not only influencing theories, but are driving huge-scale particle physics experiments and astronomical observations. This demonstrates the exceptional relevance of a third research direction that has the potential to alter these activities fundamentally.
This course is based on this third new research direction, co-pioneered by the lecturer, that aims at understanding the dark sources on the basis of a more realistic description of the Universe, i.e. it remains within General Relativity, and it does not postulate new sources in the energy-momentum tensor. It challenges the priors of the standard model, for example the conjecture that the average properties of the Universe are well-described by a homogeneous solution (the standard model). The impact of inhomogeneities on average properties of the Universe is called 'cosmological backreaction'.
The course will present in an elementary way the relevant notions in both Newtonian gravity and General Relativity. We shall need only a few aspects of these theories to derive cosmological models. We then look at average properties like the average expansion of the Universe and show that, without any restricting assumptions, we arrive at more general cosmological models. These models contain additional terms that can act as Dark Energy on large scales, but also as Dark Matter on smaller scales, thus unifying physically the 'dark sector'. We shall study these additional 'backreaction terms' and discuss important related questions.
Since a couple of years this research direction enjoys a strongly growing popularity. It has been the subject of special issues of leading journals in the field, and is regularly the object of conferences and workshops. Popularity is not only met at the level of the professionals but also in the broad audience.
04-08.12.2017 /
Thomas Buchert (ERC PI, CRAL) :
ARTHUS ROUND TABLE I
This first round table focusses on (i) nonperturbative modeling aspects of backreaction, (ii) the fundamental question of closure of the averaged equations, (iii) the generalization of the averaged equations themselves, (iv) topological and geometrical issues, both in mathematical cosmology approaches and in statistical measurements of observational data,
and finally on other fundamentals concerning, e.g., strategies for light cone averaging and light cone smoothing.
The general idea of this round table is to give the core team members and our guests a complete overview over the project structure and its workpackages, emphasizing open problems in some selected cases, and to provide near-future perspectives. The headline is to pose the good questions that allow to find the good answers.
Participants (alphabetic): Léo Brunswic, Thomas Buchert, Mauro Carfora, Martin J. France, Étienne Jaupart,
Pierre Mourier, Jan J. Ostrowski, Pratyush Pranav, Nezihe Uzun, Quentin Vigneron, Rolf Walder, David L. Wiltshire.
04.12.2017 /
Jan. J. Ostrowski (LIO Postdoc, CRAL) :
The mass function in relativistic cosmology
The realistic description of cosmological structure formation is an important challenge from both theoretical and numerical point of views. This can be partially answered via the cosmological mass function, which is a statistical tool describing a number density of collapsed objects as a function of initial conditions, mass and redshift.
In my presentation I will give a prescription for a semi-analytic treatment of structure formation and a resulting mass function on galaxy cluster scales for a highly generic scenario. This approach relies on scalar averaging of Einstein's equations together with the relativistic generalization of Zel'dovich's approximation serving as a closure condition, and thus allows one to calculate in addition mass-dependent distributions of kinematical backreaction and averaged scalar curvature. Comparison with the N-body-inferred results will also be presented.
04.12.2017 /
Quentin Vigneron (ERC Internship ENS, CRAL) :
Cosmological Dark Matter as a morphon field
Backreaction terms can be viewed as arising from an effective scalar field, called morphon field. A simple example of such a field is the scaling solution (kinematical backreaction and average scalar curvature being powers of the volume scale factor). This solution can describe models of quintessence for Dark Energy. It, however, always requires Cold Dark Matter in addition to the baryonic matter. Thus, trying to describe Dark Energy and Dark Matter with a single morphon field using a scaling solution is not possible. I describe here, how a partitioning of both the space and the morphon field could solve the problem and allow us to describe the expansion rate without Dark Energy and Dark Matter in a unified way.
04.12.2017 /
Jan. J. Ostrowski (LIO Postdoc, CRAL) :
The Green-Wald conjecture and its aftermath
In a series of papers by Green and Wald, the authors claimed to have developed a
formalism to properly describe the influence of density inhomogeneities on
background properties of the Universe, i.e., the cosmological backreaction effect.
Their main conclusion is that backreaction is trace-free and obeys the weak energy condition, i.e. it cannot mimic
Dark Energy. The applicability of Green and Wald's formalism to cosmology was criticized by a
number of cosmologists and relativists, which launched a debate among the wider community. Recent numerical investigations, as well as some explicit analytic examples show that Green and Wald's main theorem is at least not general, and in any case not applicable to cosmological backreaction in its present form.
In my talk I give a brief introduction into the Green and Wald formalism, point out the major drawbacks and attempts to put this formalism into work, and I summarize the current status of the 'backreaction debate'.
05.12.2017 /
David L. Wiltshire (Univ. of Canterbury, New Zealand) :
Cosmological averages, observables and spacetime structure
Solving the fitting problem requires a geometrical understanding
of the averages in inhomogeneous cosmology as they affect light
propagation, and their relation to measurements. In my view
foundational physical questions must be addressed. The appropriate
mathematical ingredients are an open question.
05.12.2017 /
Martin J. France (ERC Technician, CRAL) :
Non-Gaussianity and signatures of cosmic topology: toward a generalized model-independent analysis of the CMB?
Our recent Minkowski functional analyses of the CMB show that, seen in the framework of the LCDM model, the observed CMB is still highly Gaussian. But, model-independent Hermite expansions fit better the CMB Non-Gaussianity than the prescriptions of perturbation theory. We find also that more than 1 percent of a huge LCDM model sample of CMB maps is 2 to 3 times less Gaussian than the Planck map.
In order to widen the view on interpretation of both the CMB Non-Gaussianity and the CMB signatures of cosmic topology, I discuss as a proposal whether a part of the CMB dipole or/and some multipoles could be considered as being a consequence of the deviation of the CMB support manifold from the ideal sphere.
05.12.2017 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Topological holes and their persistence
Topological and morphological studies of cosmic density fields have a long history, with the Euler characteristic and Minkowski functionals playing the key role in analysis. However, the information contained in the Euler characteristic is compressed, due to the Euler-Poincare formula, which states that the Euler characteristic is the alternating sum of another topological invariant called the Betti numbers. The rest of the Minkowski functionals are more geometric in nature and provide morphological assessment of the cosmic fields. Furthermore, these descriptors are not equipped to handle the hierarchical nature of structure formation and evolution in the Universe.
In view of these observations, I will present a brief introduction to homology and persistence, and Morse theory. Stemming from algebraic topology, homology quantifies the topological characteristics of a manifold in terms of the presence of topological holes of different dimensions present in it. The topology of a d-dimensional manifold can be expressed in terms of k-dimensional holes, where k runs from 0 to d. Mathematically, these holes represent the homology groups of the manifold, and the Betti numbers are the ranks of the homology groups, counting the number of independent holes. Persistence homology is an extension of the regular homology theory in hierarchical settings. The hierarchical aspects of persistence are achieved by creating a filtering of the manifold, such that the sub-manifold at higher density threshold is contained in sub-manifolds at lower thresholds through inclusion, thereby creating a continuous map. The central tenet of persistence lies in the idea of formation and destruction of topological holes, as the density threshold changes continuously. Due to its hierarchical nature, persistence homology may be a powerful descriptor of the topology of cosmic fields, when model discrimination is the primary focus.
At the end I present an analysis of the Planck CMB temperature field.
06.12.2017 /
Pierre Mourier (PhD, CRAL) :
Fluid-comoving generalizations of the GR scalar spatial averaging formalism to arbitrary foliations
In a first part I will present a generalization of the spatial averaging formalism for inhomogeneous scalars as exposed by T. Buchert in two papers in 2000-2001. This averaging process was carried out in a fluid-orthogonal foliation for a universe model filled with irrotational dust or an irrotational perfect fluid with pressure. I will show how this can be extended to averaging in arbitrary spatial hypersurfaces, which also allows the treatment of a fully general fluid, that is, in general, non-perfect and with vorticity. Although several proposals for such a generalization have already been introduced in the literature, contrary to these our formalism sticks to the crucial concept of an averaging domain following the fluid flow and, thus, preserving its fluid rest-mass content along its evolution.
In a second part I will present the averaging operation and the system of averaged scalar Einstein equations for two different averaging definitions. The first one is directly inspired from the existing literature, modifying mostly the domain's propagation, while the second approach roots instead the averaging operator itself to the fluid flow. This latter choice allows for simple and transparent averaged and effective equations without loss of generality. I will then make use of the foliation and shift freedom to highlight an especially physically relevant particular choice, dubbed the Lagrange picture, which makes the averaged equations even simpler and removes an otherwise generally present interpretation subtlety. I will, however, point out a mathematical difficulty lying in the construction of the corresponding foliation.
07.12.2017 /
Léo Brunswic (ERC Postdoc 08.01.2018, CRAL) :
Closure with the Gauss-Bonnet-Chern-Avez theorem?
Following Magni, we present how the Gauss-Bonnet formula closes the 2+1 averaging framework of self-gravitating dust, and how the topology relates to the universal expansion: the Euler characteristic behaves as a mass which can be negative. Then, we generalize the Gauss-Bonnet-Chern theorem to 3+1 self-gravitating dust using a sandwich approach and a method of Avez. The formula we obtain does not close the averaging framework in dimension 3+1 but gives an interesting relation between a Weyl tensor invariant, the second moment of the density and extrinsic curvature scalar invariants.
07.12.2017 /
Nezihe Uzun (Univ. of Prague, Czech Republic) :
On the reciprocity relation for light propagation through multiple geometries
The reciprocity theorem of Etherington is used in cosmology in order to relate angular diameter distance to luminosity distance. It is applicable for light propagation within a single spacetime geometry and it holds irrespective of the distribution of the matter fields. Here I will consider the light propagation within multiple geometries which are not isometric to each other. I will mainly focus on the applicability of the reciprocity relation for Swiss-cheese-like cosmologies and its observational outcomes.
26.01.2018 /
Jan. J. Ostrowski (LIO Postdoc, CRAL) :
Cosmological mass function
The realistic description of cosmological structure formation is an important challenge from both theoretical and
numerical point of views. In my presentation I will give a brief prescription for a semi-analytic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. This will be obtained by 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. Some results related to the
'silent universe' model will be also presented.
30.01.2018 /
Michel Mizony (Univ. Lyon1, Camille Jordan Institute of Mathematics, France) :
What is our Universe now? - For a century of a formula written by Willem de Sitter
Starting with the Friedmann-Lemaître metric of an isotropic model universe,
we give the radially inertial form of this metric which is a generalized Gullstrand-Painlevé form of metric. The equivariant stress-energy tensor is convenient because it has straightforward interpretation in terms of velocity and potential. For each model for the Universe, the osculating manifold is a de Sitter model. Moreover, if the model universe is the open cone of a big bang event, then this de Sitter model is an open, accelerated, one. We confront this model with local observations, taking into account the observed SNIa and the Hubble parameter H(z) for redshifts z up to 2. The recent data on H(z) provide a tool to estimate cosmological parameters for the de Sitter models and their Milne limits; we fi nd:
Ho = 65 + 2 km/s/Mpc, Omega_o = 0.05 + 0.02 and an age = 15.2 + 0.3 Gyr. In other words, our model universe would only contain baryonic matter. This work can be viewed as an update of a marvelous de Sitter paper (1917-1918) about his metric.
09.05.2018 /
Thomas Buchert (ERC PI, CRAL) and Jan. J. Ostrowski (Postdoc LIO, CRAL) :
Tutorial: mass function
This tutorial focusses on themes at the interface of the ERC ARThUs group and the AstroENS Team. The aim is to
initialize a PhD topic. Foundations of Lagrangian effective models and the application to Newtonian and
relativistic backreaction models, in particular concentrating on the mass function, will be discussed.
Participants (alphabetic): Thomas Buchert, Gilles Chabrier, Étienne Jaupart, Jan. J. Ostrowski.
28.05.2018 /
Jan. J. Ostrowski (LIO Postdoc, CRAL) :
Green and Wald formalism: the aftermath of the 'backreaction debate' (Invited Talk at 'CosmoBack', Marseille, France)
In a series of papers by Green and Wald, the authors claimed to have developed a
formalism to properly describe the influence of density inhomogeneities on
background properties of the Universe, i.e., the cosmological backreaction effect.
Their main conclusion is that backreaction is trace-free and obeys the weak energy condition, i.e. it cannot mimic
Dark Energy. The applicability of Green and Wald's formalism to cosmology was criticized by a
number of cosmologists and relativists, which launched a debate among the wider community. Recent numerical investigations, as well as some explicit analytic examples show that Green and Wald's main theorem is at least not general, and in any case not applicable to cosmological backreaction in its present form.
In my talk I give a brief introduction into the Green and Wald formalism, point out the major drawbacks and attempts to put this formalism into work, and I summarize the current status of the 'backreaction debate'.
29.05.2018 /
Thomas Buchert (ERC PI, CRAL) :
Averaging Problem and Backreaction (Invited Lecture at 'CosmoBack', Marseille, France)
In this lecture I introduce the foundations of the averaging problem and cosmological backreaction. Chapters were divided into: (i) Averaging scalars for flow-orthogonal foliations; (ii) Averaging of general fluids on general foliations; (iii) Backreaction in (quasi-)Newtonian cosmology?; (iv) Closure assumptions; (v) Scalar field analogy and exact scaling solutions; (vi) Dark Energy-free Models and Observational Tests.
14.06.2018 /
Quentin Vigneron (CRAL) :
Topological acceleration in non-flat spaces
The topological acceleration is the effect of a nontrivial topology of the Universe on the gravitational field created by a point mass. The calculation of this acceleration can be done either with a Newtonian approach or a relativistic approach (e.g. Korotkin et al. (1994), Roukema et al. (2006), Ostrowski et al. (2012), Steiner (2016)). The former has the advantage of being easily implemented for various types of topological spaces. However, the Newtonian theory of gravitation is only valid for flat spaces, thus we should not be able to describe topological acceleration in spherical or hyperbolic spaces with this theory. A generalized theory of Newtonian gravity would be, however, interesting to develop and could have a number of applications, e.g. for N-body simulations, fast analytical estimates of gravitational dynamics in non-flat spaces. From this perspective, Roukema et al. (2009) used an heuristic approach in order to increase the domain of validity of Newton's theory for any spaces and calculated the topological acceleration in spherical spaces.
In a first part, I show that the approach of Roukema et al. leads to unphysical results. Then, I present in the second part what I think is a proof that a Newtonian theory on non-flat spaces is not possible. The last part presents a fully relativistic calculation of topological acceleration in a specific spherical space. The calculation is not finished but attempts to show that static topological acceleration in spherical spaces is possible, contrary to the results of Bentivegna et al. (2012).
28.06.2018 /
Thomas Buchert (ERC PI, CRAL) :
Is Dark Energy simulated by structure formation in the Universe?
(Invited Talk at '2nd World Summit on Exploring the Dark Side of the Universe', Pointe-à-Pitre, Guadeloupe)
The standard model of cosmology rests on a homogeneous-isotropic solution of Einstein's laws of gravitation. The so-called "concordance model" with homogeneous geometry fixes the parameters of this model in conformity with available observational data. Accepting this model leads to a number of unresolved issues related to the conjecture of existence of Dark Matter and Dark Energy. To resolve these, a large community either seeks to generalize the laws of gravitation, or assumes the existence of new fundamental fields providing challenges for particle physics.
In this talk we focus on a third possibility that is conservative by not generalizing the laws of Einstein and by not including any new fundamental field. We present and motivate from first principles a set of effective (i.e. spatially averaged) Einstein equations that govern the regional and global dynamics of inhomogeneous cosmological models. In this framework there are new terms that arise from curvature invariants of the inhomogeneous geometry of spatial hypersurfaces. These terms qualitatively play the role of Dark Matter and Dark Energy. We also put observational predictions of backreaction models into perspective.
05.07.2018 /
Francesco Sartini (ENS-M1) :
Globally static and stationary inhomogeneous cosmologies
Einstein's static model, which first has motivated the introduction of the cosmological constant, was abandoned soon after its formulation, as a result of the observation of the expansion of the Universe. This decision has been based on the simplistic view that any part of the Universe should reproduce the global behaviour. This is no longer valid in inhomogeneous cosmologies, where we can still have a globally static, and also stationary solution (i.e., expanding at constant speed), even without a cosmological constant. Using Buchert's averaging formalism, and a volume-partitioning method, we try to investigate the possibility of a regional expansion that could comply with observation, within a globally static or stationary Universe, ending by pointing out some remarkable differences between the two cases.
10.07.2018 /
Célia Desgrange (ENS-L3) :
Averaged inhomogeneous cosmology: fit to Supernovae without Dark Energy
Unlike the standard model of cosmology which considers the Universe to be locally homogeneous, the averaged inhomogeneous model takes into account these inhomogeneities called backreaction in order to be closer to the reality. We tested the averaged model with one of the largest currently available Type Ia supernovae data catalogue, the JLA (Joint Light-curve Analysis) catalogue. This kind of supernovae is still the only direct evidence for Dark Energy in the Universe according to the standard model.
By using exact scaling solutions parametrized with the scaling index n for the averaged curvature
and backreaction, we find n = -1.05 and a dimensionless contribution to the energy budget of
the matter parameter Ω_D0 = 0.237, results independent of the Hubble function on the domain
of averaging. In this work, we conclude that the averaged model without Dark Energy is indistinguishable from the ΛCDM model on these data, as the AIC (Akaike Information Criterion) is equal to 0.35.