Related papers: Cosmic crystallography: the euclidean isometries
We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy…
We construct an exact relativistic cosmology in which an inhomogeneous but isotropic local region has fractal number counts and matches to a homogeneous background at a scale of the order of $10^2$ Mpc. We show that Einstein's equations and…
The probability that high-redshift sources are gravitationally-lensed with large image separations (i.e., greater than can be produced by galactic deflectors) is determined by the cosmological population of group- and cluster-sized halos.…
Clusters of galaxies are used in a variety of ways to do cosmology. Some of them are presented here. Their X-ray emitting gas allows us to determine the baryon fraction, dark matter distribution and the matter density $\Omega_{m}$ of the…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
In the last years the direct measurement of cosmic rays received a push forward by the possibility of conducting experiments on board long duration balloon flights, satellites and on the International Space Station. The increase in the…
Simulations of molecular clouds often begin from highly idealised initial conditions, such as a uniform-density sphere with an artificially imposed turbulent velocity field. While the resulting structures may appear qualitatively similar to…
Multi-connected Universe models with space idenfication scales smaller than the size of the observable universe produce topological images in the catalogs of cosmic sources. In this review, we present the recent developments for the search…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting…
The determination of supersymmetric parameters at the LHC in favorable as well as difficult scenarios is presented. If discovered and measured at the LHC and the ILC, supersymmetry may provide a link between collider physics and cosmology.
Due to our vantage point in the disk of the Galaxy, its 3D structure is not directly accessible. However, knowing the spatial distribution, e.g. of atomic and molecular hydrogen gas is of great importance for interpreting and modelling…
The increasing detection of new molecules in the interstellar medium (ISM) shows that stereoisomerism is a fundamental contributor to interstellar molecular complexity. This work presents the first comprehensive overview of interstellar…
Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute…
The polarization of the cosmic microwave background radiation will have a distribution of singularities and anti-singularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities…
Clusters of galaxies are important targets in observationally cosmology, as they can be used both to study the evolution of the galaxies themselves and to constrain cosmological parameters. Here we report on the first results of a major…
We study the possible singularities of isotropic cosmological models that have a varying speed of light as well as a varying gravitational constant. The field equations typically reduce to two dimensional systems which are then analyzed…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…