Speakers 

The Complexity of the Cosmos on very large scales: relativistic, wide-angle and the ‘finger of the observer’ effects

There are multiple reasons for which galaxy clustering requires a proper general relativistic description.

 (i) We observe events lying on our past light-cone.

 (ii) The propagation of light is affected by the presence of inhomogeneities in the matter distribution.

 (iii) In consequence, galaxy observables (i.e. redshift, flux in some wave-band and angular position on the sky) are influenced by the large-scale structure intervening between the source and the observer. 

However, when we interpret observations we use an unperturbed FRW model to translate redshifts and fluxes into distances and absolute luminosities. This leads to redshift-space distortions, i.e. the reconstructed galaxy density does not coincide with the actual one. The most important source of the discrepancy is the correction due to the peculiar velocity gradient (Kaiser 1987) but it is long known that there are additional contributions and that they might become significant at large angular separations. 

Robust models of galaxy clustering on large scales should thus include these modifications that, most likely, will be key to extracting unbiased information on the dark sector of the Universe (i.e. on the nature of dark energy and dark matter) and to improve constraints on primordial non-Gaussianity.

Recent studies based on analytical calculations and on the Fisher information matrix have concluded that signatures of these additional corrections should be detectable with the next generation of wide-angle surveys. These studies have demonstrated the existence of several additional corrections that, although suppressed on smaller scales, might generate observable signals on distances comparable with the Hubble radius

In this talk I will discuss the LIGER  (LIght cones using GEneral Relativity) method, a numerical technique to build mock galaxy catalogues including all general relativistic corrections at linear order in the cosmological perturbations. LIGER post processes the output of a Newtonian simulation and combines its snapshots at constant background time to build the galaxy distribution in comoving redshift space

Finally I will discuss how the impact of observer velocity on the galaxy clustering measurements is often neglected or only corrected at the redshift level for spectroscopic surveys. In particular, using the LIGER method I will show the impact of the dipole on the monopole of the power spectrum and that it is possible to use the same dipole imprinted on the power spectrum of the galaxy to measure the expansion of the Universe.

Data Driven tools for Complex Flows

TBA

Discreteness effects, chaos, noise and the continuum limit of self gravitating models

In this talk I will review the role of discreteness effects and chaos on the relaxation of stellar systems. In particular, I will discuss the chaoticity of the N-body problem as a function of the particle number N and its implication on the validity of the continuum limit.

On the kinetic theory of self-gravitating systems: the possible role of initial correlations

I discuss the assumptions that underpin the derivation of the kinetic theory of self-gravitating bodies from the point of view of phase space distributions (Liouville equation and BBGKY hierarchy) and empirical measures (Klimontovich equation). Using the first approach, I elucidate the necessity of vanishing initial correlations for the validity of the common picture based on Vlasov violent relaxation and successive slow evolution of two-body correlations. The second approach, when rephrased in the modern language of large deviations theory, may cast light on the potentially overlooked role of nonstandard initial conditions.

On the existence of real-time path integrals

Interference is among the most universal phenomena in physics, as exemplified by the famous Feynman path integral describing quantum physics as a sum over histories. However, conditionally convergent oscillatory integrals are often delicate to define and even more difficult to evaluate. Moreover, the real-time Feynman path integral is still lacking a mathematically rigorous definition. In this talk, I will show steps towards defining the Feynman's path integral non-perturbatively, without a Wick rotation to imaginary time. I start by introducing a class of smooth regulators rendering the interference integral absolutely convergent. Subsequently, I continue the integration domain to its Lefschetz thimble associated with its relevant instantons. The resulting set of integrals can be formally defined in terms of the infinite-dimensional Wiener measure developed for the theory of Brownian motion. As I will show, the resulting real-time path integral is organized by caustics, unlike the Euclidean version. I will illustrate this approach by studying Pöschl-Teller quantum mechanics and the path integral for gravity.

Symplectic quantization: a new deterministic approach to the dynamics of quantum fields inspired by statistical mechanics

The present work is about a new method to sample the quantum fluctuations of relativistic fields by means of a pseudo-Hamiltonian dynamics in an enlarge space of variables. The proposed approach promotes the fictitious time of Parisi-Wu stochastic quantisation to a true physical parameter controlling a deterministic dynamics. The sampling of quantum fluctuations is guaranteed by the presence of new additionational conjugated momenta, which reprents the rate of variation of ordinary fields with respect to the newly added time variable. The main goal of this approach is to provide a numerical method to sample quantum fluctuations of fields directly in Minkowski space, whereas all existent methods allowed one so far to do this only in Euclidean space, therefore loosing important physics. From the pseudo-Hamiltonian dynanamics one is then able, assuming ergodicity, to retrieve the Feynman path integral as the Fourier transform of a pseudo-microcanonical partition function. The whole framework proposed is not only the source of a new numerical approach to study quantum fields but also and most importantly reveals important connections between quantum field theory, statistical mechanics and Hamiltonian dynamics. Here we will discuss the main ideas behind the formalism and the first succesful results of numerical tests, as well as the difficulties we encountered.

Calorimetry of a Schwarzschild-deSitter geometry (and nonequilibrium effects in cosmology)

We address the question on how to associate heat with geometry, and we discuss the example of a Schwarzschild black hole in a de Sitter background.  As we are effectively dealing there with a two-temperature system  (as temperatures are associated both to the black hole and to the cosmic horizon), not only issues of thermal physics are arising but also the more general question is asked concerning nonequilibrium effects in cosmology and about geometric dissipation.  Therefore,  time permitting, we will make some remarks concerning the dark energy puzzle, the possibility of a space roar and about the heat capacity of a graph.

Squeezing out New Physics from Large Scale Structure data

I will present some new directions towards the optimal and model independent extraction of information from the Large Scale Structure of the Universe. After reviewing the present state of the art approaches to galaxy clustering in LCDM, I will discuss how symmetries can be exploited to cover more general theoretical landscapes in a model independent way. Then, I will motivate the increasing interest in new statistics beyond the two and third order correlation functions, and highlight some of their strong points and some issues to be understood before they can be reliably modelled from a theoretical point of view.

New (complex) physics from Pulsar Timing Array? 

The direct detection of gravitational waves by the LVK collaboration open a new and exciting window into our late and early universe. Recently, the PTA collaboration claim the detection of a stochastic gravitational wave background. However, the origin of this signal is still unclear and the physics behind more complex than what we tought. In this talk I will discuss the possibile interpretations of this signal and the information that we can extract about our universe.

Quantum Field Theory of dark matter

A tentative quantum field theory of dark matter is discussed. The oversimplified model is built up by coupling the field of a spinless massive particle (a wimp) with the field of a spinless, non massive one.  The minimal Lagrangian coupling is of the Yukawa type. The Lorentz invariant model thus obtained belongs to the family of the so-called Klein-Gordon-Wave ones. Our KGW model turns out to be ruled, when written in dimensionless form, by one parameter only: the ratio m_P/m of the Planck mass to the wimp mass, to which there corresponds a well determined space scale L of the fields. There are two regimes in the model. The first one corresponds to m_P/m of order one. In this case the stationary states of the model are determined by a time independent Schroedinger-Poisson system, with eigenvalues determining a discrete spectrum of m, in particular yielding a lower bound to m. In this case the fields extend on a space scale L of the order of the Planck one. The other regime corresponds to m_P/m much greater than one. In such a case, a Hamiltonian perturbative approach leads to deduce the Schroedinger-Wave system, where dark matter is approximately conserved and non relativistic. Here the fields extend on a space scale L below the Mpc for masses above the GeV, and some details of the excited stationary states of the system appear to be compatible with the form of the galaxy rotation curves.

Statistical mechanics of shell-shaped Bose-Einstein condensates  on board of the International Space Station

Motivated by the recent achievement of ultracold shell-shaped atomic gases in microgravity on board of the International Space Station [1], we investigate the thermodynamics of a Bose-Einstein condensate on the surface of a sphere [2,3]. We determine analytically the critical temperature and the condensate fraction of a noninteracting Bose gas. Then we consider the inclusion of a zero-range interatomic potential, extending the noninteracting results at zero and finite temperature by using a path integral approach [2]. Both in the noninteracting and interacting cases the crucial role of the finite radius of the sphere is emphasized, showing that in the limit of infinite radius one recovers the familiar two-dimensional results [2]. We also investigate the Berezinski-Kosterlitz-Thouless transition driven by the proliferation of quantized vortices on the surface of the sphere, analyzing the interplay of condensation and superfluidity in this finite-size system [2,3]. We describe the occurrence of this topological transition by conceptually extending the theory of Berezinskii, Kosterlitz, and Thouless to our finite-size system [3]. Finally, considering the general topic of low-dimensional quantum gases in curved spatial geometries, we delineate the study of vortices, the few-body physics, and the search for analog models in various curved geometries as the most promising research areas [4]. 

[1] C.R. Carollo et al. Observation of ultracold atomic bubbles in orbital microgravity, Nature 606, 281-286 (2022).

[2] A. Tononi and L. Salasnich, Bose-Einstein Condensation on the Surface of a Sphere, Phys. Rev. Lett. 123, 160403 (2019).

[3] A. Tononi, A. Pelster, and L. Salasnich, Topological superfluid transition in bubble-trapped condensates, Phys. Rev. Res. 4, 013122 (2022).  

[4] A. Tononi and L. Salasnich, Low-dimensional quantum gases in curved geometries, Nat. Rev. Phys.  5, 398–406 (2023).

Large-deviations statistics of the cosmic density field – from complexity to simplicity

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, like the number of trials or random components of a system or the variance of the fluctuations. It is a versatile theory with a wide-range of applications from finance to statistical mechanics and cosmology. In this context, deep analogies can be made between concepts of statistical physics, such as the entropy and the free energy, and concepts of large deviation theory having more technical names, such as the rate function and the scaled cumulant generating function. I will describe how a large-deviations principle can be used to follow the gravitational evolution of the large scale structure of matter in the Universe into the nonlinear regime. When looking at a cosmological statistics with in-built symmetry, key mathematical theorems allow to simplify the path integral linking initial (or linear) and final (nonlinear) statistics following steepest-descent arguments. This allows us to predict key non-Gaussian features of the late-time matter density field from first principles with exciting potential to probe fundamental physics with upcoming galaxy surveys in a new regime.

Why is the Universe spatially flat? Some clues from the renormalization group

Evidence for almost spatial flatness of the Universe has been provided from several observational probes, including the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) from galaxy clustering data. However, other than inflation, and in this case only in the limit of infinite time, there is no strong a priori motivation for a spatially flat Universe. Using the renormalization group (RG) technique in curved spacetime, we present in this work a theoretical motivation for spatial flatness. Starting from a general spacetime, the first step of the RG, coarse-graining, gives a Friedmann-Lemaître-Robertson-Walker (FLRW) metric with a set of parameters. Then, we study the rescaling properties of the curvature parameter, and find that zero spatial curvature of the FLRW metric is singled out as the unique scale-free, non-singular background for cosmological perturbations.

Two different integration methods for the Schrödinger-Poisson Equation as a Model for Cold Dark Matter

We compare two different numerical methods to integrate in time spatially delocalized initial distributions of fuzzy dark matter. The basic equation is a nonlinear Schrödinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling non-relativistic gravity.  Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing realistic dark matter formation over cosmologically relevant scales.