21.09.2021 /
Léo Brunswic (ERC Postdoc, CRAL) :
Notes on the relative Yamabe invariant of
punctured manifolds of non-positive type and application to inhomogeneous cosmology (Seminar: University of Avignon, France)
In collaboration with Thomas Buchert we propose a new model to
compute the deviation of the real Universe from the standard model of
cosmology. The model estimates the deviation in terms of the Einstein-Hilbert
energy of space-like slices (leaves of a Riemannian foliation of a
Lorentzian manifold), together with further hypotheses in terms of the relative
Yamabe invariant of these leaves. The relative Yamabe invariants,
introduced by Akutagawa and Botvinnik, are generalizations of the Yamabe
invariant for manifolds with boundaries. Their computation is often
challenging, especially in the positive curvature case. We focus on
finding upper bounds for the relative Yamabe invariant of Riemannian
punctured tori by assuming some coarse geometric knowledge of the
manifold and its boundary (volume, diameter, ...). We give some physical
motivations and some background on the relative Yamabe invariants,
state a conjecture for such upper bounds with qualitative arguments and
prove a weaker result supporting the conjecture.
30.09.2021 /
Asta Heinesen (ERC Postdoc, CRAL) :
Observing the Universe without expectations (Seminar: University of Stavanger, Norway)
Cosmological data is typically analyzed under the assumption that the Universe is well described as being spatially homogeneous and isotropic. However, the level of applicability of this ansatz on various scales of cosmological observation remains to be tested. The increasing precision in cosmological data will allow us to perform better tests of our models and to carry out model-independent data analysis.
I will present cosmographic strategies for inferring properties of the Universe without making assumptions about the metric of spacetime or the field equations prescribing it.
I will discuss standardizable objects and redshift drift signals as model-independent probes of the kinematics of our Universe.
12.10. and 15.10.2021 /
Asta Heinesen (ERC Postdoc, CRAL) :
Anisotropic cosmography (Seminar: University of Zürich and University of Geneva, Switzerland)
Cosmological data is typically analyzed under the model assumptions of exact homogeneity and isotropy over preferred spatial sections of the Universe. However, the level of applicability of such assumptions on various scales of cosmological observation is not directly quantifiable with available data, and remains an ansatz of cosmological data analysis.
I will present cosmographic strategies for inferring properties of the Universe without making assumptions about the metric of spacetime or the field equations prescribing it.
I will discuss standardizable objects and redshift drift signals as model-independent probes of the kinematics of our Universe.
27.10.2021 /
Asta Heinesen (ERC Postdoc, CRAL) :
Anisotropic cosmography (Online Seminar: COSMOPRINCIPLE, Seoul, Korea)
Cosmological data is typically analyzed under the model assumptions of exact spatial homogeneity and isotropy in the spacetime description of our Universe. However, such symmetries are in reality broken due to the presence of cosmic structure. I will present cosmographic strategies for analyzing data while remaining agnostic about the form of the metric of spac-time and the field equations prescribing it.
I will discuss standardizable objects and redshift drift signals as model-independent probes of the kinematics of our Universe. The developed framework allows for consistent analyses of anisotropic features in cosmological data.
07.04.2022 /
Ismael Delgado Gaspar (NCBJ Warsaw, Poland) :
Beyond the Relativistic Zel'dovich Approximation: an exact-solution controlled model for structure formation
Motivated by the correspondence between the Relativistic Zel'dovich Approximation (RZA) and Szekeres Class II exact solutions, we propose a generalization of RZA that includes the entire Szekeres family. In contrast to RZA, that retains a global cosmological background, the proposed method contains a space-dependent reference model obeying
Friedmann-like evolution equations. The overall approach is then interpreted as the evolution of a deformation field on an inhomogeneous Friedmann-like reference model that includes backreaction.
In this scheme, the most relevant exact cosmological solutions emerge as particular sets of the initial data.
Finally, some numerical examples illustrate the application potential of this approach.
27.04.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Novel data analysis strategies for large cosmological datasets (Online Seminar: Portsmouth, UK)
Cosmological data is typically analyzed under the model assumptions of exact spatial homogeneity and isotropy in the spacetime description of our Universe. However, such symmetries are in reality broken due to the presence of cosmic structure. I will present cosmographic strategies for analyzing data, while remaining agnostic about the form of the metric of spacetime and the field equations prescribing it.
I will discuss standardizable objects and redshift-drift signals as model-independent probes of the kinematics of our Universe. The developed frameworks allow for consistent analyses of anisotropic features in cosmological data.
06.05.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Expanding on Hubble's law (Observatoire de Lyon, France)
A century ago, Lemaitre, Slipher and Hubble discovered an approximate proportionality law between distances and redshifts to astrophysical sources in our cosmic vicinity. This proportionality law is today referred to as Hubble's law (or the Hubble-Lemaitre law) and is central to much modern cosmological data analysis, where it is used to determine the expansion of our Universe. Hubble's law might be viewed as an isotropic and lowest order Taylor series expansion of distances around the observer. When the universe is not perfectly isotropic and when astrophysical sources span a large range of distances, the Hubble law breaks down as an approximation for distances. I will describe how to expand on the Hubble law in order to consistently take into account effects of anisotropy when analyzing modern cosmological data.
08.-14.05.2022 /
Thomas Buchert (ERC PI, CRAL) :
ARTHUS ROUND TABLE VIII
This round table is organized on the occasion of a workshop at
IESC Cargèse, Corsica, France. The following talks have been scheduled.
Participants (alphabetic): Thomas Buchert, Ismael Delgado Gaspar (Warsaw, Poland), Martin J. France, Asta Heinesen, Mikolaj Korzynski (Warsaw, Poland, Online), Jan J. Ostrowski (Warsaw, Poland), Pratyush Pranav, Dennis Stock (Geneva, Switzerland), Roland Triay (Marseille, France), and Nezihe Uzun.
12.05.2022 /
Ismael Delgado Gaspar (NCBJ Warsaw, Poland) :
Beyond Relativistic Zel'dovich Approximation: a new method for structure formation
Motivated by the correspondence between the Relativistic Zel'dovich Approximation (RZA) and Szekeres exact solutions, we propose a generalization of RZA that includes the entire Szekeres family. In contrast to RZA, which retains a global cosmological background, the proposed scheme contains a space-dependent scale factor, resulting from a Friedmann-like reference model. The overall approach is then interpreted as the evolution of a deformation field on the reference model. This method, by construction, contains the most relevant exact cosmological solutions as particular cases. We implement illustrative numerical examples and estimate the error from the violation of the constraint equations.
12.05.2022 /
Jan J. Ostrowski (NCBJ Warsaw, Poland) :
Relativistic Structure Formation
In my talk I will present some of the constituents of the modern cosmology, the structure formation process and the spatial curvature estimates, focusing on the methods of modeling gravitational instability evolution and calculating its statistical outcome. These formalisms are based on the Buchert scalar averaging formalism, with the Zel'dovich approximation serving as a closure condition and the silent universe models (Einstein equations with no rotation and no energy transfer). Both of these methods are utilizing Einstein's theory of general relativity and reveal substantial differences compared with the standard Newtonian or post-Newtonian treatments. The resulting relativistic mass functions of galaxy clusters will be presented. Possible applications and improvements will be briefly discussed.
12.05.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Anisotropic Cosmography
Cosmological data is typically analyzed under the model assumptions of exact spatial homogeneity and isotropy in the spacetime description of our Universe. However, such symmetries are in reality broken due to the presence of cosmic structure. I will present cosmographic strategies for analyzing data while remaining agnostic about the form of the metric of spacetime and the determining field equations.
I will discuss standardizable objects and redshift-drift signals as model-independent probes of the kinematics of our Universe. The developed frameworks allow for consistent analyses of anisotropic features in cosmological data.
12.05.2022 /
Martin J. France (ERC Technician, CRAL) :
CMB properties in a Universe with multiply connected topology
The LambdaCDM model implicitly assumes infiniteness of the spatial sections of our Universe. However, the observation map of the CMB temperature anisotropies presents a lack of correlation at large angular scale in the 2-point correlation function, i.e. beyond 60 degrees.
In my talk I shall present another CMB signature, statistical, compatible with the multi-connectedness of the Universe, the 3-torus topological manifold. I introduce a new statistical measure that consolidates a size of our Universe to be around three Hubble lengths. I will also discuss a linear dependence between the torus-length and the new statistical measure.
I shall then illustrate my talk with results obtained over large ensembles of CMB simulation maps, in the infinite
LambdaCDM universe model and five different sizes of universe models with 3-toroidal topology.
12.05.2022 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Anomalies in the topology of the fluctuations in the Cosmic Microwave Background
Cosmology is transitioning from a theoretical discipline towards one with increased focus on observations, resulting in a massive surge of data that demands increasingly more sophisticated methods to glean meaningful information. In a related development, geometry and topology have witnessed a tilt from purely theoretical fields towards strong focus on application. A foray into 'big data' quickly brings to front two of the central statistical challenges of our times: detection and classification of structure in extremely large, high-dimensional data sets. Among the most intriguing new approaches to this challenge is 'TDA', or topological data analysis, the primary aim of which is providing topologically informative pre-analyses of data, which serve as input to more quantitative analyses at a later stage. Algebraic and computational topology at the level of homology and persistent homology are the foundational pillars of TDA.
In the first part of my talk, I will give a summary of the theoretical and computational aspects of topological data analysis. In the second part, I will present an analysis of the topological properties of the temperature and polarization maps of the Cosmic Microwave Background (CMB) radiation obtained by the Planck satellite. I will also discuss some of the anomalies that the temperature and polarization maps exhibit with respect to the simulations based on the standard cosmological model, which assumes the initial fluctuation field to be an instance of an isotropic and homogeneous Gaussian random field.
12.05.2022 /
Mikolaj Korzynski (CFT Pan Warsaw, Poland) :
Parallax in General Relativity
I will discuss the general problem of parallax measurement in general relativity. The parallax effect can be used to define the parallax distance, one of possible distance measures to distant objects in GR. I will show how the tiny difference between the angular diameter distance and the parallax distance can be used to measure the matter content along the line of sight and how the sign of this difference is related to the null energy condition. I will also briefly discuss possible applications of these results to astrometry and cosmology.
12.05.2022 /
Dennis Stock (University of Geneva, Switzerland) :
The Hawking energy of a cosmic observer in linearly perturbed FLRW
Addressing cosmological questions exclusively based on observations requires a formulation on the past light cone of the cosmic observer. In this talk, the question of how to define gravitational energy associated with the past light cone of a cosmic observer is studied by introducing Hawking's quasi-local energy as a tentative energy measure of the observable Universe. The Hawking energy phenomenologically quantifies energy in terms of light bending. This talk will mainly focus on the relation of the Hawking energy to cosmological observables within linear perturbation theory on an FLRW background.
17.05.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Blind analysis of cosmological data (University of Montpellier, France)
In cosmology, data is typically analyzed under the model assumptions of exact spatial homogeneity and isotropy in the spacetime description of our Universe. However, such symmetries are in reality broken due to the presence of cosmic structure.
I will present strategies for doing blind analysis of cosmological data, where no assumptions about the form of the metric of spacetime or the field equations determining it are made. In particular, the developed frameworks allow for arbitrary inhomogeneity and anisotropy in the observer's cosmic vicinity.
I will discuss standardizable objects and redshift-drift signals as model-independent probes of the kinematics of our Universe. The developed frameworks allow for consistent analyses of anisotropic features in cosmological data.
18.05.2022 /
Ismael Delgado Gaspar (NCBJ Warsaw, Poland) :
Beyond the Zel'dovich Approximation in relativistic cosmology (Online Seminar: Atlantic General Relativity 2022; University of Newfoundland and Labrador, Canada)
Motivated by the correspondence between the Relativistic Zel'dovich Approximation (RZA) and Szekeres Class II exact solutions, we propose a generalization of RZA that includes the entire Szekeres family. In contrast to RZA, which retains a global cosmological background, the proposed method contains a space-dependent reference model obeying
Friedmann-like evolution equations. The overall approach is then interpreted as the evolution of a deformation field on an inhomogeneous Friedmann-like reference model that includes backreaction. In this scheme, the most relevant exact cosmological solutions emerge as particular sets of the initial data. Finally, some numerical examples illustrate the application potential of this approach.
24.05.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Blind analysis of cosmological data (University of Cambridge, UK)
A century ago, Lemaitre, Slipher and Hubble discovered an approximate proportionality law between distances and redshifts to astrophysical sources in our cosmic vicinity. This proportionality law is today referred to as Hubble's law (or the Hubble-Lemaitre law) and is central to much modern cosmological data analysis, where it is used to determine the expansion of our Universe. Hubble's law might be viewed as an isotropic and lowest order Taylor series expansion of distances around the observer. When the Universe is not perfectly isotropic and when astrophysical sources span a large range of distances, Hubble's law breaks down as an approximation for distances. I will describe how to expand on Hubble's law in order to consistently take into account effects of inhomogeneity and anisotropy when analyzing modern cosmological datasets.
25.05.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Blind analysis of cosmological data (Queen Mary University of London, UK)
In cosmology, data is typically analyzed under the model assumptions of exact spatial homogeneity and isotropy in the spacetime description of our Universe. However, such symmetries are in reality broken due to the presence of cosmic structure. I will present frameworks for blind analysis of cosmological data, where no assumptions about the form of the metric of spacetime or the field equations determining it are made.
I will discuss standardizable objects and redshift drift signals as model-independent probes of the kinematics of our Universe. The developed frameworks allow for consistent analyses of anisotropic features in cosmological data.
26.05.2022 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Geometry and topology: Applications to cosmological datasets (Online APEC Seminar: Kavli IPMU, Tokyo, Japan)
Cosmology is transitioning from a theoretical discipline towards one with increased focus on observations, resulting in a massive surge of data that demands increasingly more sophisticated methods to glean meaningful information. In a related development, geometry and topology have witnessed a tilt from purely theoretical fields towards strong focus on application. A foray into 'big data' quickly brings to front two of the central statistical challenges of our times -- detection and classification of structure in extremely large, high-dimensional, data sets. Among the most intriguing new approaches to this challenge is 'TDA', or topological data analysis, the primary aim of which is providing topologically informative pre-analyses of data, which serve as input to more quantitative analyses at a later stage. Algebraic and computational topology at the level of homology and persistent homology are the foundational pillars of TDA. These developments on the topological side are recent, and add value to the already existing geometric tools and methodologies employed in investigating the cosmological fields.
In the first part of my talk, I will present a summary of the theoretical and computational aspects of topological data analysis. In the second part of the talk, I will present an analysis of the topological properties of the temperature and polarization maps of the Cosmic Microwave Background (CMB) radiation obtained by the Planck satellite. I will also discuss some of the anomalies that the temperature and polarization maps exhibit with respect to the simulations based on the standard cosmological model, which assumes the initial fluctuation field to be an instance of an isotropic and homogeneous Gaussian random field.
21.06.2022 /
Niels Fardeau (M1 Internship student) :
Non-perturbative 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 more strongly 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 non-collisional 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, non-perturbative approach, and various approximations of the derived model are then compared numerically. These results are finally extended to a 3D case without symmetries, and master equations are derived for the evolution of all parts of the perturbations, including a nonlinear wave equation for the trace part of its gradient.
21.06.2022 /
Aubin Courty (M1 Internship student) :
Inhomogeneous Cosmology in Spherical Space
We look at inhomogeneous cosmology in the context of general relativity, and consider an exact two-scale partitioning of the spatial sections at constant time. Assuming global stationarity of the universe model, we need one more condition to close the averaged Einstein equations, a closure that may be derived from properties of the whole spatial section. We work with spherical space forms with multiply connected topology, and we look at some general properties including harmonic oscillations of the CMB anisotropies best-fit Poincaré Dodecahedral Space. We then try to infer a closure condition on the two-scale volume partitioning with harmonic oscillations. We also look at an application for the simulation of structure formation in quotiented spherical spaces using the Relativistic Zel'dovich Approximation, initialized by eigenmodes of the considered space forms.
28.06.2022 /
Martin J. France (ERC Technician, CRAL) :
CMB properties in a Universe with simply or multiply connected topology
(PHD thesis defence)
One of the motivations of my thesis work was to specify and characterize some drifts and anomalies of the observed CMB compared to the predictions of the current concordance model, the LCDM model. This model is globally satisfactory, nevertheless, among the cosmological observations interpreted within this model, several remain in anomaly or in tension with it. My thesis confirms through new methods of analysis that classes of universe models, spatially finite, globally anisotropic and statistically compatible with the LCDM model, solve the anomaly of lack of large-scale CMB correlations.
18.07.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Expanding on Hubble's law (Online Seminar: Kapteyn Astronomical Institute, The University of Groningen, The Netherlands
A century ago, Lemaitre, Slipher and Hubble discovered an approximate proportionality law between distances and redshifts to astrophysical sources in our cosmic vicinity. This proportionality law is today referred to as Hubble's law (or the Hubble-Lemaitre law) and is central to much modern cosmological data analysis, where it is used to determine the expansion of our Universe. Hubble's law might be viewed as an isotropic and lowest order Taylor series expansion of distances around the observer. When the Universe is not perfectly isotropic and when astrophysical sources span a large range of distances, Hubble's law breaks down as an approximation for distances. I will describe how to expand on Hubble's law in order to consistently take into account effects of inhomogeneity and anisotropy when analyzing modern cosmological datasets.
22.07.2022 /
Thomas Buchert (ERC PI, CRAL) :
On general-relativistic Lagrangian perturbation theory (Observatory of Vienna, Austria)
The Newtonian Lagrangian perturbation theory is a widely used framework to study structure formation in cosmology. We review a general-relativistic formulation of such a perturbation approach that can be obtained via a simple dictionary from the Newtonian approach. We then spend some time to introduce the concept of spatially averaging the Einstein equations, discuss some properties of the averaged system and compare with its Newtonian counterpart, also summarizing known theorems on integral properties of cosmological models. Following from these considerations, we provide an average model for the general-relativistic Lagrangian perturbation models.
We discuss subcases of exact solutions related to Szekeres Class II and flat LTB models, serving as a motivation to go beyond Lagrangian perturbation theory on a global homogeneous-isotropic background cosmology. We present ongoing work on a new exact-solution controlled approximation that does not involve a global reference background - a genuine property of general relativity - and it contains Szekeres class I and, on average, non-flat 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.