05.09.2022 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Anomalies in the topology of the Cosmic Microwave Background
(Challenges to LCDM, Aristotle University of Thessaloniki, Greece)
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. Understanding these anomalies may be crucial towards understanding the tensions in parameter estimation within the standard model framework.
20.09.2022 /
Thomas Buchert (ERC PI, CRAL) :
ARTHUS ROUND TABLE IX
This small round table is organized jointly with the researchers from the Physics Department, ENS-Lyon, to discuss mutual interests around the following scheduled talk by Marc Geiller.
Participants (alphabetic): Hamed Barzegar, Thomas Buchert, Marc Geiller, Martin J. France, Asta Heinesen, Sucheta Majumdar, Hugo Roussille, Nezihe Uzun.
20.09.2022 /
Marc Geiller (ENS Physics Department) :
Asymptotic symmetries in general relativity
I will review recent results in the study of the asymptotic structure of general relativity, explain the various extensions of the boundary symmetry group which have been proposed in the literature, and their role in classical and quantum gravity.
28.09.2022 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Topological (Big) Data Analysis: From biology to cosmology
and beyond (ECOSS 35, Luxembourg)
Modern scientific endeavors are increasingly becoming data-centric across a spectrum of scientific disciplines, including cosmology and astrophysics, biomedical sciences, material and drug discovery, and finances, to name a few. The increased focus on data has simultaneously led to a massive surge in data collection across disciplines, such that the term Big Data has entered common parlance. The advent of Big Data has simultaneously brought to front two of the central statistical challenges of our times: the detection and classification of structure in extremely large,
high-dimensional, data sets, demanding increasingly more sophisticated methods to detect pattern and glean meaningful information. Among the most intriguing new approaches to this challenge is TDA, or Topological Data Analysis, one of the primary aims of which is providing non-metric, but topologically informative, pre-analyses of data which make later, more quantitative, analyses feasible. 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 computational geometric tools and methodologies employed in investigating the data in various fields, such as the Minkowski functionals. Apart from presenting tools for data analysis, topo-geometrical formalisms also provide for methods resulting in state-of-the-art visualization techniques that are based on strong mathematical foundations.
This talk will have two distinct parts devoted to the theoretical background and experimental applications respectively. In the first part of my talk, I will present a summary of the theoretical and computational aspects of geometry and topology from the view point of data analysis. TDA and computational geometry has been used effectively in a variety of scenarios in biomedical sciences. Consequently, in the second part of the talk, I will highlight applications by presenting examples from biological and cosmological datasets. I will begin with discussing the topological characteristics of gene replication, by examining the replication timing data from a few human cell-lines and discuss the relevance of topo-geometrical methods with respect to existing methods of analysis in the field. As a second example, I will present an analysis of the topological properties of the temperature and polarization maps of the (CMB) radiation obtained by the Planck satellite. The CMB radiation represents the earliest visible light in the Universe, and contains a treasure trove of information about the initial conditions of the Universe. The CMB also represents the largest canvas on which to test the fundamental assumptions of the cosmological principle. Within this context, I will discuss some of the anomalies that the CMB 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.
18.10.2022 /
Pratyush Pranav (ERC Postdoc, CRAL) :
Testing the cosmological principle through topological properties of cosmic microwave background fluctuations (TIFR Mumbai, India)
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 geometry and topology from the view point of data analysis. Subsequently, 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. The CMB radiation represents the earliest visible light in the Universe, and contains a treasure trove of information about the initial conditions of the Universe. The CMB also represents the largest canvas on which to test the fundamental tenets of the cosmological principle. Within this context, I will discuss some of the anomalies that the CMB 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.
21.11.2022 /
Asta Heinesen (ERC Postdoc, CRAL) :
Excess dimming of light from supernovae in a Universe with ordinary matter? (Euclid Workshop, Online)
I will discuss the theoretical possibility of reconciling modern cosmological observations with a general-relativistic Universe without dark energy.
13.12.2022 /
Francesco Sartini (Visitor, CRAL) :
Schrödinger symmetry in cosmology and hydrodynamics
Homogenous cosmological models belong to classes of space-time metrics defined in terms of a finite number of degrees of freedom, for which the Einstein-Hilbert action reduces to a one-dimensional mechanical model. We show that these actions have a set of Noether charges generating the centrally extended Schrödinger group as dynamical symmetry. This group is also shared by the non-compressible Navier-Stokes equation and the non-linear Gross-Pitaevskii equation. This allows to build a map between hydrodynamics and cosmological dynamics. Beyond the mathematical analogy, the existence of these symmetries corroborates the view of cosmological dynamics as emerging from quantum condensates. Still, it might also have significant consequences for the study of cosmological perturbations.
15.03.2023 /
Asta Heinesen (ERC Postdoc, CRAL) :
Dimming of light in general relativity: On the possible emergence of dark energy effects in space-times with ordinary matter (University of Helsinki, Finland)
Can modern cosmological observations be reconciled with a general-relativistic Universe without an anti-gravitating energy source? Usually, the answer to this question by cosmologists is in the negative, and it is commonly believed that the observed excess dimming of supernovae relative to that in the Milne model is evidence for dark energy. This intuition can be shown to be correct within Friedmann-Lemaitre-Robertson-Walker space-times. In this talk I will illustrate that there is no fundamental result in general relativity that prevents the excess dimming of light in space-times satisfying the strong energy condition, once the Friedmann-Lemaitre-Robertson-Walker symmetries are broken. This opens up an avenue of research into general-relativistic space-time solutions without dark energy that may be competitive cosmological models. I will discuss the geometrical constraints that such space-times must satisfy in order to conform with cosmological observations.
19.04.2023 /
Asta Heinesen (ERC Postdoc, CRAL) :
Dimming of light in general relativity: On the possibility of explaining cosmological observations without dark energy (University of Lisbon, Portugal)
Can modern cosmological observations be reconciled with a general-relativistic Universe without an anti-gravitating energy source? Usually, the answer to this question by cosmologists is in the negative, and it is commonly believed that the observed excess dimming of light from supernovae relative to the predictions of the Milne model is evidence for dark energy. In this talk I will illustrate why this intuition does not generally hold once the symmetries of the Friedmann-Lemaitre-Robertson-Walker metric are broken. This opens up an avenue of research into general-relativistic space-time solutions without dark energy that may be competitive cosmological models. I will discuss the geometrical constraints that such space-times must necessarily satisfy in order to conform with cosmological observations.
22.06.2022 /
Thomas Buchert (ERC PI, CRAL) :
ARTHUS ROUND TABLE X
This round table is held in the week from 22nd of June till 28th of June with informal discussions.
The following talks have been scheduled.
Participants (alphabetic): Hamed Barzegar (CRAL), Léo Brunswic (Shanghai), Thomas Buchert (CRAL), Doris Folini (Zurich), Martin J. France (CRAL), Asta Heinesen (CRAL), Etera Livine (ENS Physics), Sucheta Majumdar (ENS Physics), Jan J. Ostrowski (Warsaw, Poland), Roberto A. Sussman (Mexico), Nezihe Uzun (Poland), Rolf Walder (CRAL) and David L. Wiltshire (New Zealand).
26.06.2023 /
David L. Wiltshire (University of Canterbury, New Zealand) :
Cosmic expansion versus motion: Probing the difference
General inhomogeneous cosmologies give rise to differential cosmic expansion which differs from that of Friedmann-Lemaitre-Robertson-Walker (FLRW) models. Even models with an average isotropic homogeneous isotropic expansion law on > 100/h Mpc scales will generically have expansion laws which differ from FLRW plus local Lorentz boosts. That is they differ from the conventional "kinematic interpretation". Strong evidence (~ 5.1 sigma) against the kinematic interpretation has been provided by Secrest et al (2022) combining the Ellis-Baldwin test on 1.36 million distant quasars with similar studies of radio galaxies. There is a correlation with CMB anomalies.
Such signatures are a generic expectation in models which differ from FLRW, exhibiting backreaction, including the timescape cosmology. The particular features of nonkinematic differential expansion, regardless of the backreaction scheme, can be isolated by constructing toy Lambda-Szekeres models which asymptote to FLRW/Lambda CDM on > 100/h Mpc scales but exhibit nonkinematic differential expansion on smaller scales.
In this talk I will discuss ongoing work with the goal of constraining such toy models by local peculiar-velocity data, and then using such models to probe the Ellis-Baldwin test, which in itself challenges the standard cosmology.
26.06.2023 /
Roberto A. Sussman (UNAM Mexico, Mexico) :
Advances in probing the gravitational entropy proposals adaptable to structure formation in Cosmology
I would like to summarize and present published research and recent attempts to advance cosmological applications of two proposals of Gravitational entropy, which are distinct from the standard holographic approach and from the entropy of the sources. One is the proposal by Clifton-Ellis and Tavakol (CET) based on the Bel-Robinson tensor, the other by Hosoya and Buchert (HB), based on the Leibler-Kullbach functional of Information Theory. We have successfully applied these proposals to inhomogeneous dust solutions of Einstein's equations (LTB and Szekeres models), finding that they predict equivalent entropy growth in regions with structure formation (over-densities and voids), but CET is local and HB is non-local. The CET proposal provides an interesting interpretation of the cosmological constant as an asymptotic finite entropy saturation value. Currently we are looking at the application of these proposals to different 4-velocity frames and spacetimes that are not Petrov type D.
26.06.2023 /
Asta Heinesen (ERC Postdoc, CRAL) :
Dimming of light in general relativity: On the possible emergence of dark energy effects in space-times with ordinary matter
Can modern cosmological observations be reconciled with a general-relativistic Universe without an anti-gravitating energy source? Usually, the answer to this question by cosmologists is in the negative, and it is commonly believed that the observed excess dimming of light from supernovae relative to the predictions of the Milne model is evidence for dark energy. In this talk I will illustrate why this intuition does not generally hold once the symmetries of the Friedmann-Lemaitre-Robertson-Walker metric are broken.
This opens up an avenue of research into general-relativistic space-time solutions without dark energy that may be competitive cosmological models. I will discuss the geometrical constraints that such space-times must necessarily satisfy in order to conform with cosmological observations.
27.06.2023 /
Nezihe Uzun (CFT Pan Warsaw, Poland) :
Hydrodynamic interpretation of minimum uncertainty states
In this talk, we aim at exploring certain connections between classical and quantum systems in phase space.
As the minimum uncertainty states are the closest one can get to a classical picture, squeezed coherent states are the main actors of this investigation.
On the other hand, hydrodynamic interpretation of quantum mechanics, which is mathematically equivalent to the de Broglie-Bohm approach, provides connections between the classical and the quantum worlds in a very intuitive manner. Here, we show that once one considers the hydrodynamic interpretation of squeezed coherent states in tandem with the Wigner-Weyl-Moyal approach, a dynamic equilibrium thermodynamics of a quantum system can be derived quite easily, similar to the one in classical kinetic theory.
28.06.2023 /
Léo Brunswic (Huawei Shanghai, PR China) :
The Yamabe Gap as a measure of inhomogeneity
Buchert equations for averaged dust cosmologies may be written to relate the evolution of the scale factor of a space slice to its averaged scalar curvature. The latter may be seen as the only unknown source term in the equation, and the FLRW model is being recovered adding the ansatz that this averaged curvature follows a power law proportional to the inverse square of the scale factor. Relating the average curvature to the scale invariant normalization of the Einstein-Hilbert action, we show that the so-called relative Yamabe invariants provide bounds on the behavior of the scalar curvature source term under looser hypotheses than isotropy and homogeneity of the standard model. The Yamabe gap measuring the difference of the dynamics of the scale factor between a reference FLRW and the given space slice is shown to have constant sign under our hypotheses. In particular we show that expansion is always faster than in a FLRW model.
28.06.2023 /
Hamed Barzegar (ERC Postdoc, CRAL) :
Some remarks on the construction principles of warp-drive spacetimes
Observational cosmology begins to look at global anisotropies in various data, but also related theoretical considerations on "dipole cosmologies" are surfacing.
Related formalisms have been vividly discussed in the context of so-called
warp-drive spacetime. A brief discussion is offered on the current construction
of warp-drive metrics, including critical assessments and possibilities of improvement.
26.07.2023 /
Hamed Barzegar (ERC Postdoc, CRAL) :
Basics of warp-drive (CRAL conference: Chalet de la Hulotte)
I will provide a brief discussion of the genealogy and pathology of the so-called warp-drive spacetimes. Additionally, time permitting, I will explain our proposal to precisely address the existing issues and approach them effectively within the context of General Relativity.