Evolution of density and velocity profiles of matter in large voids

We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark energy - are continuous media with ideal fluid energy-momentum tensors, which interact only gravitationally. Equations of the evolution of perturbations in the comoving to cosmological background reference frame for every component are obtained from equations of conservation and Einstein's ones and are integrated by modified Euler method. Initial conditions are set at the early stage of evolution in the radiation-dominated epoch, when the scale of perturbation is mush larger than the particle horizon. Results show how the profiles of density and velocity of matter in spherical voids with different overdensity shells are formed.Comment: 9 figure

Wasserstein distance as a new tool for discriminating cosmologies through the topology of large scale structure

In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present root-mean-square matter fluctuation averaged over a sphere of radius 8 Mpc comoving). The Wasserstein distance (a.k.a. the pair-matching distance) was proposed to measure the difference between two networks in terms of persistent homology. The advantage of this approach consists in its non-parametric way of probing the topology of the Cosmic web, in contrast to graph-theoretical approach depending on linking length. By treating the halos of the Cosmic Web as points in a point cloud we calculate persistent homologies, build persistence (birth-death) diagrams and evaluate Wasserstein distance between them. The latter showed itself as a convenient tool to compare simulated Cosmic webs. We show that one can discern two Cosmic webs (simulated or real) with different $\sigma_8$ parameter. It turns out that Wasserstein distance's discrimination ability depends on redshift $z$, as well as on the dimensionality of considered homology features. We find that the highest discriminating power this tool obtains at $z=2$ snapshots, among the considered $z=2$, $1$, and $0.1$ ones.Comment: submitted to Monthly notices of the royal astronomical societ

Samuil Kaplan and the development of astrophysical research at the Lviv University (dedicated to the 100th anniversary of his birth)

Samuil Kaplan (1921-1978) was a productive and famous astrophysicist. He was affiliated with a number of scientific centers in different cities of former Soviet Union. The earliest 13 years of his career, namely in the 1948-1961 years, he worked in Lviv University in Ukraine (then it was called the Ukrainian Soviet Socialist Republic). In the present paper, the Lviv period of his life and scientific activity is described on the basis of archival materials and his published studies. Kaplan arrived in Lviv in June 1948, at the same month when he obtained the degree of Candidate of science. He was a head of the astrophysics sector at the Astronomical Observatory of the University, was a professor of department for theoretical physics as well as the founder and head of a station for optical observations of artificial satellites of Earth. He was active in the organization of the astronomical observational site outside of the city. During the years in Lviv, Kaplan wrote more than 80 articles and 3 monographs in 9 areas. The focus of his interests at that time was on stability of circular orbits in the Schwarzschild field, on white dwarf theory, on space gas dynamics, and cosmic plasma physics, and turbulence, on acceleration of cosmic rays, on physics of interstellar medium, on physics and evolution of stars, on cosmology and gravitation, and on optical observations of Earth artificial satellites. Some of his results are fundamental for development of theory in these fields as well as of observational techniques. The complete bibliography of his works published during the Lviv period is presented. Respective scientific achievements of Samuil Kaplan are reviewed in the light of the current state of research in these areas.Comment: 24 pages, 5 figures; accepted for publication in Europian Physical Journal

Large-scale structures in the ΛCDM Universe: network analysis and machine learning

International audienceWe perform an analysis of the cosmic web as a complex network, which is built on a Λ cold dark matter (ΛCDM) cosmological simulation. For each of nodes, which are in this case dark matter haloes formed in the simulation, we compute 10 network metrics, which characterize the role and position of a node in the network. The relation of these metrics to topological affiliation of the halo, i.e. to the type of large-scale structure, which it belongs to, is then investigated. In particular, the correlation coefficients between network metrics and topology classes are computed. We have applied different machine learning methods to test the predictive power of obtained network metrics and to check if one could use network analysis as a tool for establishing topology of the large-scale structure of the Universe. Results of such predictions, combined in the confusion matrix, show that it is not possible to give a good prediction of the topology of cosmic web (score is ≈70 |${{\rm per\ cent}}$| in average) based only on coordinates and velocities of nodes (haloes), yet network metrics can give a hint about the topological landscape of matter distribution