Related papers: Cosmic crystallography: the hyperbolic isometries
The pair separations statistical methods devised to detect the topology of the universe rely on the accurate knowledge of the three-dimensional positions of the cosmic sources. The determination of these positions, however, involves…
The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly…
In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely…
The CMB anisotropy depends sensitively upon the slope and amplitude of primordial density and gravitational wave fluctuations, the baryon density, the Hubble constant, the cosmological constant, the ionization history, {\it etc.} We report…
We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results…
In addition to shear and vorticity a homogeneous background may also exhibit anisotropic curvature. Here a class of spacetimes is shown to exist where the anisotropy is solely of the latter type, and the shear-free condition is supported by…
A mathematical model of the Universe evolution, based on asymmetric doublet of classical and phantom dcalar Higgs fields with a kinetic connection between the components, has been constructed and studied. A detailed qualitative analysis was…
Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved)…
We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…
A numerical likelihood approach to the determination of cosmic ray anisotropies is presented which offers many advantages over other approaches. It allows a wide range of statistically meaningful hypotheses to be compared even when full sky…
We investigate the subgroup structure of the hyperoctahedral group in six dimensions. In particular, we study the subgroups isomorphic to the icosahedral group. We classify the orthogonal crystallographic representations of the icosahedral…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
Galactic accretion interacts in complex ways with gaseous halos, including galactic winds. As a result, observational diagnostics typically probe a range of intertwined physical phenomena. Because of this complexity, cosmological…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote…
Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made…
Direct measurements of cosmic ray (CR) species combined with observations of their associated gamma-ray emissions can be used to constrain models of CR propagation, trace the structure of the Galaxy, and search for signatures of new…
A cosmological model with total density close to critical (and flat geometry), dominated by dark matter and dark energy of unknown nature, and consistent with the basic predictions of the inflationary scenario is a very good fit to a…
In this paper, we introduce a new generalization of Pascal's triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regular mosaics on the hyperbolic plane. We describe precisely the…
Resent works of Hawking and Susskind suggested that information is conserved in the universe. We extend this thesis and propose that dynamics of information - computations can conserve in Anti-de-Sitter cosmological model. Information…