Related papers: Cosmic crystallography: the hyperbolic isometries
Cosmic crystallography is based on the principle that peaks in the pair separation histogram (PSH) of objects in a catalogue should be induced by the high number of topologically lensed pairs that are separated by Clifford translations, in…
Science opportunities and recommendations concerning optical/infrared polarimetry for the upcoming decade in the field of cosmology. Community-based White Paper to Astro2010 in response to the call for such papers.
This article shows that the compactified Milne universe geometry, a toy model for the big crunch/big bang transition, can be realized in hyperbolic metamaterials, a new class of nanoengineered systems which have recently found its way as an…
The cosmological principle states that our Universe is statistically homogeneous and isotropic at large scales. However, due to the relative motion of the Solar System, an additional kinematic dipole can be detected in the distribution of…
We present a modified version of the cosmic crystallography method, especially useful for testing closed models of negative spatial curvature. The images of clusters of galaxies in simulated catalogs are ``pulled back'' to the fundamental…
The spatial distribution of the gaseous components of the Milky Way is of great importance for a number of different fields, for example, Galactic structure, star formation, and cosmic rays. However, obtaining distance information to…
We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of…
Large deviation statistics is implemented to predict the statistics of cosmic densities in cylinders applicable to photometric surveys. It yields few percent accurate analytical predictions for the one-point probability distribution…
An isometry is a geometric transformation that preserves distances between pairs of points. We present methods to classify isometries in the Euclidean plane, and extend these methods to spherical, single elliptical, and hyperbolic geometry.…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
It is pointed out that if we allow for the possibility of a multilayered universe, it is possible to maintain exact supersymmetry and arrange, in principle, for the vanishing of the cosmological constant. Superpartner(s) of a known particle…
We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results…
Rapid progress has been made in observations of the temperature anisotropies of the Cosmic Microwave Background (CMB). These observations have enabled cosmologists to characterize the state of the universe at recombination, and…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
The isoperimetric problem is one of the oldest in geometry and it consists of finding a surface of minimum area that encloses a given volume $V$. It is particularly important in physics because of its strong relation with stability, and…
We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different…
We investigate the relativistic cosmological hydrodynamic perturbations. We present the general large scale solutions of the perturbation variables valid for the general sign of three space curvature, the cosmological constant, and…
New, large, ground and space telescopes are contributing to an exciting and rapid period of growth in observational cosmology. The subject is now far from its earlier days of being data-starved and unconstrained, and new data are fueling a…
In this article, we study the geometry of an infinite dimensional Hyperbolic space. We will consider the group of isometries of the Hilbert ball equipped with the Carath$\acute{e}$odory metric and learn about some special subclasses of this…
An axiomatic approach to the mathematical models of the isotropic cosmology.