15.10.2020 /
Quentin Vigneron (PhD, CRAL) :
Backreaction in the Galilei limit of general relativity?
The type of global topology in cosmology is known to play a role in the global expansion of the Universe. With the rise of the inhomogeneous cosmology, which studies the effect (called backreaction) of inhomogeneities on the expansion, there is a lifting of degeneracy between the specific topologies in each type. The question will then be: in an inhomogeneous Universe, does the specific type of topology affects the expansion?
By starting from the only known result between topology and expansion, the Buchert-Ehlers theorem, we will show that we can reframe the question as: is there a Newtonian limit with spatial curvature? This will be the first part of this talk. The second part will focus on a possible answer to this question.
20.10.2020 /
Thomas Buchert (ERC PI, CRAL) :
ARTHUS ROUND TABLE VI
This small round table mainly focusses on discussions. We only scheduled the following two talks.
Participants (alphabetic): Léo Brunswic, Thomas Buchert, Martin J. France, Jan J. Ostrowski, Pratyush Pranav, Nezihe Uzun, and Quentin Vigneron.
20.10.2020 /
Léo Brunswic (ERC Postdoc, CRAL) :
On a recent paper of Galloway, Khuri and Woolgar
We present and discuss the preprint "The Topology of General
Cosmological Models" that uses a generalization of Myers' theorem to
obtain a constraint on the topology of the Universe from CMB data. The
line of argumentation is outlined, then the limitations of the
hypotheses and of the interpretation of the data is discussed.
Comparison with an ongoing project of the team on Yamabe functional constraints is
given as well as an attempt to correct the limitations of the present paper to make it more physically relevant.
20.10.2020 /
Quentin Vigneron (PhD, CRAL) :
Backreaction induced by topology
The Buchert-Ehlers theorem states that backreaction is zero in Newtonian theory. This result is often used to say that if the late Universe has a locally Newtonian dynamics, then global backreaction should be negligible and could not explain dark energy. This is only true if the topology of the Universe is the same as in Newton's theory, i.e. an Euclidean topology. The Universe could however be locally Newtonian but with a non-Euclidean topology, as authorized by general relativity. In this case the Buchert-Ehlers theorem might not hold anymore. Using the Newton-Cartan formulation, we show that Newton's equations can be written such that they are formally equivalent to the 1+3 evolution and constraint equations of general relativity. By heuristically introducing a spatial curvature to this system of equations, we allow for non-Euclidean types of topologies, while having a Newtonian dynamics on domains small with respect to this curvature. We show that in the case of a spherical or hyperbolic topology, backreaction is not anymore zero, and thus is induced by the topology. This backreaction is directly linked to the bulk velocity of the fluid: an expected behaviour. It also depends on both extrinsic and intrinsic curvature invariants. Thus, observing local Newtonian dynamics in the late Universe does not rule out backreaction as an explanation for dark energy. Inverting the argument, dark energy might be a signature of a non-Euclidean global topology. While the heuristic approach used to derive these results is not yet obtained from a well-defined limit of general relativity, we give some strategies to define such a limit.
14.12.2020 /
Asta Heinesen (ERC Postdoc, CRAL) :
Redshift drift in general space-times - model independent mapping of the expansion history of the Universe (Online Seminar: Christchurch, New Zealand)
I will discuss the formulation of redshift drift for general universe models. I will focus on modifications to the Friedmann-Lemaitre-Robertson-Walker (FLRW) prediction for redshift drift signals due to the presence of cosmic structure. An important realization is that redshift drift cannot in general be thought of as a direct probe of the average expansion rate of the Universe due to the presence of structure along the light beams from the astrophysical sources to the observer. Furthermore, a dipolar and a quadrupolar offset in the detection of redshift drift for observers placed in locally anisotropic environments is expected.
05.02.2021 /
Asta Heinesen (ERC Postdoc, CRAL) :
Frameworks for model-independent data analysis - towards a cosmology founded on observations (Online Seminar: DAMTP Cambridge, UK)
Since the advent of general relativistic cosmology a century ago, cosmology has progressed from the extrapolative study of a sparse number of astrophysical sources to a precise investigation of the origin and evolution of the Universe. However, the precision in the determination of cosmological parameters in modern data analysis comes at the price of imposing strong a priori assumptions in the modeling of the largest scales of our Universe. I will present strategies for model-independent analysis of upcoming cosmological datasets, which allow to infer properties of the Universe without making assumptions about the metric of spacetime or the field equations prescribing it.
13.02.2021 /
Quentin Vigneron (PhD, CRAL) :
A non-Euclidean Newtonian limit of General Relativity (Online Seminar:
11th Central European Relativity Seminar, Vienna, Austria)
I will be interested in defining a limit from general relativity, called non-Euclidean Newtonian limit, leading to a theory which is locally equivalent to Newtonian gravitation, but with a non-Euclidean geometry. It is constructed using the geometrized limit of Dautcourt, Künzle and Ehlers, corresponding to a limit from a Lorentzian manifold, carrying solutions of the Einstein equations, to a Galilean manifold. For non-Euclidean spatial topologies to be allowed in this limit, the
stress-energy tensor in general relativity needs to feature additional source terms linked to the spatial Ricci curvature, especially an 'energy curvature' and an 'anisotropic pressure curvature'. We discuss the relevance of these terms for relativistic cosmology.
25.02.2021 /
Léo Brunswic (ERC Postdoc, CRAL) :
On singular (G,X)-manifolds and branched coverings (Institut Fourier, Grenoble, France)
Traditionally, a (G,X)-manifold is a manifold locally modeled on X with change of charts in G,
some Lie group acting analytically on X. In most common examples, X is a space-form and G
is its group of isometries. The strength of the theory of (G,X)-manifold comes from the 'Developing
Theorem' that allows to compare a manifold M to the model space and, in many instances, construct
a natural identification Ω / Γ ≃ M with Ω a domain of X, with Γ a
group acting on X and preserving Ω.
The study of such manifolds with singularities is common with a notion
of singularity depending on context. We present a possible starting
point for a theory unifying the notions of singularities, and we prove many
general properties allowing to manipulate singular (G,X)-manifolds with
peace of mind. We also provide a preliminary version of a 'Developing
Theorem' of singular manifolds and relevant examples as well as an
application to flat spacetimes with BTZ singularities.
03.03.2021 /
Asta Heinesen (ERC Postdoc, CRAL) :
The general luminosity distance 'Hubble law' for model-independent cosmological analysis (Online Seminar: STAG Research Centre, Southampton, UK)
Since the foundation of general relativistic cosmology a century ago, cosmological data analysis has relied on strong model assumptions in order to infer information about the properties of our Universe. I will discuss strategies for
model-independent analysis of upcoming cosmological datasets, which allow to infer properties of the Universe without making assumptions about the metric of spacetime or the field equations prescribing it. I will present the general series expansion of luminosity distance, giving rise to a generalization of the FLRW Hubble law, which can in principle be used directly for fully model-independent analyses of large cosmological surveys of standardizable objects.
29.03.2021 /
Ismael Delgado Gaspar (UNAM Mexico City, Mexico) :
Relativistic Zel'dovich Approximation and Exact Solutions (Online Seminar: 15th Iberian Cosmology Meeting, University of Coimbra, Portugal)
We examine the relationship between the Szekeres models and the Relativistic Zel'dovich Approximation (RZA). We show that the second class of the Szekeres solutions is exactly contained within the RZA when the latter is restricted to an irrotational dust source with a flow-orthogonal foliation of spacetime. In such a case, the solution is governed by the first principal scalar invariant of the deformation field, proving a direct connection with a class of Newtonian 3-dimensional solutions without symmetry. For the second class, a necessary and sufficient condition for the vanishing of cosmological backreaction is expressed through integral constraints. Domains with no backreaction can be smoothly matched, forming a lattice model, where exact deviations average out at a given scale of homogeneity, and the homogeneous and isotropic background is recovered as an average property of the model. Although the connection with the first class of Szekeres solutions is not straightforward, this class allows for the interpretation in terms of a spatial superposition of non-intersecting fluid lines, where each world line evolves independently and under the RZA model equations, but with different associated 'local backgrounds'. This hints towards a possible generalization of the Lagrangian perturbation schemes to structure formation models on evolving backgrounds, including global cosmological backreaction.
12.04.2021 /
Asta Heinesen (ERC Postdoc, CRAL) :
Frameworks for model-independent data analysis in cosmology (Online Conference: Theory of Gravitation and Variation in Cosmology I, CIRM Marseille, France)
Since the foundation of general relativistic cosmology a century ago, cosmology has progressed from the extrapolative study of a sparse number of astrophysical sources to a precise investigation of the origin and evolution of the Universe. However, the precision in the determination of cosmological parameters in modern cosmological data analysis comes at the price of imposing strong a priori assumptions in the modeling of the largest scales of our Universe via the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) universe models. In the field of inhomogeneous cosmology, the aim is to go beyond the FLRW ansatz of exact homogeneity and isotropy. I will present strategies for
model-independent analysis of upcoming cosmological datasets of standardizable objects (e.g. supernovae) and redshift drift, which allow to infer properties of the Universe without making assumptions about the metric of spacetime or the field equations prescribing it.
15.04.2021 /
Hayley Macpherson (DAMTP, Cambridge, UK) :
Numerical relativity as a tool to study inhomogeneous cosmology (Online Conference: Theory of Gravitation and Variation in Cosmology I, CIRM Marseille, France)
Numerical relativity (NR) is commonly applied to simulations of relativistic compact objects such as binary black holes or neutron stars. The application of NR to inhomogeneous cosmology is still relatively new, allowing for large-scale simulations of nonlinear structure formation without any constraints on the form of the metric of spacetime. Simulations like this will eventually allow us to answer the long-term debate on the size of the backreaction effect on cosmological expansion. In addition, we are uniquely positioned to study general-relativistic (GR) effects on cosmological observables, while remaining agnostic about the existence of any background metric model of spacetime.I will present the basics of NR and its applications to inhomogeneous cosmology over the past 5 years. I will discuss the current status of GR effects that have been studied, and discuss future prospects for further improving our methods.
16.04.2021 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Topological data analysis for cosmology: theory and applications (Online Conference: Theory of Gravitation and Variation in Cosmology I, CIRM Marseille, France)
Cosmology and 'Big data' or data analysis, of which topo-geometrical data analysis is rapidly becoming a main component, are both burgeoning and increasingly related fields at the moment. 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 applications. 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. In this lecture I will present a survey on the theoretical and computational aspects of topological data analysis at a pedagogical level, simultaneously exploring up the application component via analyses of cosmological datasets. The datasets we will focus on are the Cosmic Microwave Background data, as well as the galaxy calalogs from the SDSS.
26.05.2021 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Topological data analysis for cosmology: theory and applications (Online Conference: Algebraic and Geometric Methods of Analysis, Kiev, Ukraine)
Cosmology and Big data or data analysis, of which topo-geometrical data analysis is rapidly becoming a main component, are both burgeoning and increasingly related fields at the moment. 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 are the foundational pillars on which TDA rests. (abridged)
01.06.2021 /
Asta Heinesen (ERC Postdoc, CRAL) and Hayley Macpherson (DAMTP, Cambridge, UK) :
The luminosity distance Hubble law in a realistic anisotropic Universe and Numerical Relativity (Online Cosmology Talk)
Since the foundation of general relativistic cosmology a century ago, cosmological data analysis has relied on symmetry assumptions in order to infer information about the properties of our Universe. We will present a cosmographic representation of luminosity distance valid for general spacetimes without exact symmetries, giving rise to a generalization of the FLRW Hubble law. This generalized Hubble law can be used for fully model-independent analyses of upcoming large cosmological surveys of standardizable objects. We present a numerical relativity study in which we investigate the signatures of the generalized Hubble law in a realistic cosmological setting. We discuss our results in relation to the Hubble tension and the dark energy problem of cosmology.
06.07.2021 /
Asta Heinesen (ERC Postdoc, CRAL) and Hayley Macpherson (DAMTP, Cambridge, UK) :
The general luminosity distance 'Hubble law' for model-independent cosmological analysis (Online Seminar: 'Cosmology from Home')
Since the foundation of general relativistic cosmology a century ago, cosmological data analysis has relied on strong model assumptions in order to infer information about the properties of our Universe. We will present a cosmographic representation of luminosity distance valid for general spacetimes, giving rise to a generalization of the FLRW Hubble law, which can be used for fully model-independent analyses of upcoming large cosmological surveys of standardizable objects. We present a numerical relativity study in which we investigate the signatures of the generalized Hubble law in a realistic cosmological setting.
07.07.2021 /
Nezihe Uzun (ERC Postdoc, CRAL) :
Symplectic evolution of an observed light bundle (Online Seminar: 16th Marcel Grossmann Meeting)
Each and every observational information we obtain from the sky regarding the brightnesses, distances or image distortions resides on the deviation of a null geodesic bundle. In this talk, we will present the symplectic evolution of it on a reduced phase space. The resulting formalism is analogous to the one in paraxial Newtonian optics. It allows one to identify any spacetime as an optical device and distinguish its thin lens, pure magnifier and rotator components. We will show that the distance reciprocity in relativity results from the symplectic evolution of this null bundle. Other potential applications like wavization and quantization will also be summarized.
08.-16.07.2021 /
Thomas Buchert (ERC PI, CRAL) :
ARTHUS ROUND TABLE VII
This round table is organized on the occasion of two PhD defenses (Quentin Vigneron and Étienne Jaupart) for which a number of visitors were invited to further discuss topics of the project. We scheduled the following three talks, two of them by the internship students Antonin Borderies (M1) and Alfred Bovon (M2).
Participants (alphabetic): Antonin Borderies, Alfred Bovon, Léo Brunswic, Thomas Buchert, Célia Desgrange (former L3), Rémi Faure (former M1), Martin J. France, Asta Heinesen, Étienne Jaupart, Pierre Mourier (AEI Hannover, Germany), Boudewijn F. Roukema (Torun, Poland), Francesco Sartini (former M1), Roland Triay (Marseille, France), Nezihe Uzun, Rolf Walder and Quentin Vigneron.
15.07.2021 /
Antonin Borderies (ERC internship student M1, CRAL) :
Inhomogeneities and Anisotropies in the Universe analyzed with Supernovae of Type Ia
The standard model of cosmology is currently the most employed model to describe our Universe on average. However, to work properly it needs to introduce dark energy and dark matter, whose physical nature is yet unknown. Aiming at avoiding these unknowns, it is possible to build a more general model of cosmology (always based on the Einstein field equations) which does not adhere to the hypotheses of the standard model: the homogeneity and the isotropy of the Universe at all scales. It is possible build a new model through averaging of a general inhomogeneous model, where the influence of the inhomogeneities can potentially replace dark energy and dark matter for the description of our Universe. In this report we study the relation between the luminosity distance and the redshift z with no assumptions on the geometry and the content of space; inhomogeneities and anisotropies appear in this relation. Thus, it is possible to measure them from data of our local past light cone, notably by a numerical study of Type Ia supernovae data (the JLA catalogue) which comprise standard candles. The present study shows that we detect a strong dipole for the deceleration parameter in the direction of the CMB dipole, but the quadrupole in the generalized Hubble parameter is insignificant for the data available at the time of the internship.
15.07.2021 /
Léo Brunswic (ERC Postdoc, CRAL) :
Yamabe gap and Ricci-Yamabe flow toward a measure of
inhomogeneity-driven expansion
The scalar averaging framework provides general formulas for
the scale factor of domains at the cost of the introduction of a new
unknown: the backreaction. In the context of an irrotational dust
fluid, the dynamics of the scale factor is completely determined by the
dynamics of the average scalar curvature. However, in dimension 3 and
higher, the average scalar curvature does not follow any law as simple
as the Gauss-Bonnet theorem. We utilize recent work on the Yamabe
invariant to find constraints on the average scalar curvature.
Qualitative observations can be drawn easily going in the direction of a
deviation from the FLRW model toward expansion. This deviation is
quantified by the Yamabe gap we introduce. We describe a path toward an
effective computation of the Yamabe gap and hopefully a measure for the
contribution of inhomogeneities to expansion.
16.07.2021 /
Alfred Bovon (ERC internship student M2, CRAL) :
Backreaction and Virialization: Volume partitioning of inhomogeneous Newtonian cosmologies
During this internship, I looked at partitioned spaces of Newtonian universe models, separated into underdense and overdense regions. Using the formalism of backreaction, an interaction between the inhomogeneities of the formation of structures in the Universe and its expansion is analyzed. The point of the internship was to close the Buchert equations governing spatial averages through assumptions on the different components of the theoretical model. To do that, I made assumptions using a physical model, virialization and numerical analysis.
26., 27., 29.07.2021 /
Roberto Sussman (UNAM Mexico City, Mexico) :
Inhomogeneous Cosmological Models based on exact solutions of Einstein's equations (Online Lecture: Theory of Gravitation and Variation in Cosmology II, CIRM Marseille, France)
In this course I will present in detail research output (including my own) on theoretical and physical interpretation of various classes of exact and approximate solutions of Einstein's equations that are applicable to Cosmology. The course considers the restrictions from observational constraints, but the emphasis is more on a theoretical perspective that focuses on: (i) a covariant definition of inhomogeneities, (ii) their non-linear dynamics, (iii) the relation to cosmological perturbations, (iv) the effects of the choice of 4-velocity frames and (v) applications. Given this background knowledge, I will show how these cosmological models can serve as theoretical tools to probe and explore open problems in proposed formalisms, such as: averaging, backreaction and non-holographic gravitational entropy. The models can also be useful to describe our Cosmography at supercluster scale and to test codes in Numerical Relativity applied to Cosmology. In my lectures I will present results from published articles, as well as run Maple worksheets that compute for the models under consideration the field equations and all covariant quantities of interest.
27., 29.07.2021 /
Boudewijn F. Roukema (Nicolaus Copernicus Univ. Torun, Poland) :
Cosmic inhomogeneity and topology (Online Lecture: Theory of Gravitation and Variation in Cosmology II, CIRM Marseille, France)
The standard cosmological model is a semi-decoupled biverse model: uniform expansion in one parallel Universe affects perturbation growth in the other Universe but is forbidden by assumption from being affected in return. Instead, taking into account both expansion and structure formation simultaneously in a universe model could potentially provide an explanation of 'dark energy' within standard general relativity; the only non-standard assumption is to drop the semi-decoupling hypothesis. Inhomogeneity itself has links with the global topology of the spatial section of the Universe, which is observationally unknown, but, in principle, may reveal itself either on large scales or in local kinematics and patterns of structure.
27.07.2021 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Topo-geometrical characteristics of CMB temperature fluctuations (Online Conference: Theory of Gravitation and Variation in Cosmology II, CIRM Marseille, France)
At the epoch of recombination, matter and radiation separate, allowing radiation to stream freely in the Universe.
This free-streaming radiation permeating the Universe, that we observe as the Cosmic Microwave Background (CMB) radiation, encodes a treasure trove of information about the initial conditions in the Universe. Despite having a remarkably consistent average temperature, the CMB still exhibits tiny deviations of the order of 10 to -5 from the background average. The temperature fluctuations in the CMB trace the fluctuations in the underlying matter distribution in the infant Universe, that are linked to the spontaneous quantum fluctuations generated in an otherwise homogeneous medium. Thus studying the properties of the temperature fluctuations in the CMB is essential towards understanding the properties of the primordial matter field.
In this seminar, I will present an analysis of the topo-geometrical characteristics of the temperature fluctuations in the Cosmic Microwave Background. The topological tools employed for the analysis find their root in homology theory, which describes the topology of a D-dimensional manifold in terms of the p-dimensional cycles that bound the p-dimensional holes of the manifold, p = 0, . . . , D. Intuitively, in three spatial dimensions, the 0-dimensional cycle represents connected components separating topological gaps, the 1-dimensional cycle represents topological loops bounding holes or tunnels, and 2-dimensional cycles bound the topological voids. The geometrical part of the analysis involves tools emanating from integral geometric settings, represented by the Lipschitz-Killing curvatures (LKCs), or equivalently the Minkowski functionals, which represent the notion of volume, area, curvature length, among others. We will specifically concentrate on the D-th Minowski functional, or equivalently the 0-th LKC which is connected to the Euler characteristic, and has topological connotations, in order to facilitate a comparison with earlier results in the literature.
I will present the analysis of the final data release of Planck measurements of the CMB temperature fluctuations, while also briefly touching on earlier data releases. The main component will be the analysis of the temperature maps, while I will also briefly touch on the polarization maps for completeness. This will involve comparing the observational maps with the simulations based on the standard cosmological model, that posits the fluctuation characteristics to be that of an isotropic and homogeneous Gaussian random field.
28.07.2021 /
Pierre Mourier (AEI Hannover, Germany) :
Spatial averaging and backreaction terms on general foliations in relativistic cosmology (Online Conference: Theory of Gravitation and Variation in Cosmology II, CIRM Marseille, France)
The formation of the large-scale matter structures implies that the late-time Universe can only be homogeneous in a statistical sense. Its actual realization features nonlinear regional variations in the matter density, expansion, or spatial curvature. An effective description of its large-scale dynamics in terms of a homogeneous model or perturbations thereof therefore relies on a statistical ensemble average or a spatial smoothing of such inhomogeneities over large enough scales. Explicitly applying such a spatial averaging on scalar projections of the Einstein equations in background-free cosmological models typically leads to qualitative deviations to the Friedmannian dynamics, expressed by so-called 'backreaction' terms. In this talk, I will first briefly recall these notions of spatial averaging and backreaction within a relatively simple framework where, in particular, the spatial slices correspond to the rest frames of the model's irrotational fluid source. Investigating these effects in more general analytic models or from relativistic simulations both usually require alternative foliation choices. I will thus present a generalization of this formalism to arbitrary spatial slicings, as well as the resulting effective dynamics of comoving regions of a general fluid source. I will then discuss a manifestly covariant reformulation and its use to bound the possible variations of the averaged scalar quantities when the spatial slicing is changed. I will also mention the application of the generalized formalism to the quantitative study of the backreaction terms from recently developed relativistic cosmological simulations and present some preliminary results of such a numerical investigation.
30.07.2021 /
Mikolaj Korzynski (CFT Pan Warsaw, Poland) :
Redshift drift, position drift and trigonometric parallax in general relativity (Online Conference: Theory of Gravitation and Variation in Cosmology II, CIRM Marseille, France)
I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. With the recent advancements in astrometry, the drifts of distant sources are likely to become important observables in cosmology in the near future. In my talk I will present the derivation of exact relativistic formulas for the drifts. I will show how the drifts may be expressed in terms of the kinematical variables characterizing the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completely general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences and their possible applications to the gravitational lensing theory, cosmology and pulsar timing. Building on the same formalism I will also consider the trigonometric parallax effect in general relativity, and show how we can measure the mass density along the line of sight by comparing the parallax distance and the angular diameter distance to a single source.
30.07.2021 /
Ismael Delgado Gaspar (UNAM Mexico City, Mexico) :
Exact solutions of Einstein's equations and Relativistic Zel'dovich Approximation (Online Conference: Theory of Gravitation and Variation in Cosmology II, CIRM Marseille, France)
The current era of precision cosmology has produced a large amount of high-quality observational data at all astrophysical and cosmological scales, whose theoretical interpretation requires a robust modeling of self-gravitating systems. However, a non-perturbative approach by means of exact solutions of Einstein's equations has been less favored to analyze the cosmological observations. In this talk, we will show that the full dynamical freedom of the Szekeres models (the most general exact solution applicable to cosmology) allows for the description of realistic 3-dimensional networks of cold dark matter (CDM) structures. We will also discuss how these solutions can be generalized to give place to a new
nonlinear perturbative approach. In the first part, we will examine the sufficient conditions for the existence of multiple spatial extrema of the Szekeres covariant scalars. These results allow us to set up networks of pancake-shaped CDM overdensities and density voids, providing a coarse-grained but fully relativistic nonlinear description of large-scale cosmic structures before their virialization. The second part will examine the relationship between the Szekeres models and the Relativistic Zel'dovich Approximation (RZA). We show that the second class of the Szekeres solutions is exactly contained within RZA when the solution is governed by the first principal scalar invariant of the deformation field. Although the connection with the first class of Szekeres models is not straightforward, this class can be interpreted as a spatial superposition of non-intersecting fluid lines, where each world line evolves independently and under the RZA model equations on different associated 'local backgrounds'. Such an interpretation paves the way for generalizing the Lagrangian perturbation scheme to structure formation models containing the whole family of Szekeres models as a limit.
26.08.2021 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Topology and geometry of cosmological datasets theory and applications (RBI Zagreb, Croatia)
Cosmology and Big data or data analysis, of which topo-geometrical data analysis
is rapidly becoming a main component, are both burgeoning and increasingly related fields at
the moment. 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 are the foundational pillars on which TDA rests.
I will present a survey on the theoretical and computational aspects of topological data analysis,
simultaneously exploring up the application component via analyses of cosmological datasets.
The dataset we will focus on is of the Cosmic Microwave Background, obtained by the recently
concluded Planck mission, with a view to compare the observations with the predictions of
the standard cosmological model, that predicts the initial conditions in the Universe to be
that of an isotropic, homogeneous Gaussian random field. At the epoch of recombination
in the infant stage of the Universe, some 370,000 years after the Big Bang, matter and
radiation separate for the first time, and radiation permeates freely in the Universe.
This free-streaming radiation, that we observe as the Cosmic Microwave Background,
encodes a treasure trove of information about the initial conditions and properties of
matter distribution in the Universe.