Related papers: Topological Pattern Formation
The standard model of cosmology is based on the hot Big Bang theory and the inflationary paradigm. Recent precise observations of the temperature and polarization anisotropies in the cosmic microwave background and the matter distribution…
Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the…
The standard cosmological model does not determine the spatial topology of the universe. This article revisits the signature of a non-trivial topology on the properties of the cosmic microwave background anisotropies. We show that the…
The formation of the cosmic structures in the late Universe is considered using Vlasov kinetic approach. The crucial point is the use of the gravitational potential with repulsive term of the cosmological constant which provides a solution…
We discuss gravitational effects of global scalar fields and, especially, of global topological defects. We first give an introduction to the dynamics of global fields and the formation of defects. Next we investigate the induced…
For the first time, the combination of semi-analytic modelling of galaxy formation and N-body simulations of cosmic structure formation enables us to model, at the same time, both the photometric and the clustering properties of galaxies.…
We hypothesise that properties of space could underly some patterns observed in nature. We explore the possibility that the observed variety of matter particles and the pattern of their properties arise due to the non-orientability of the…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
If the Universe has the topology of a 3-torus ($T^3$), then it follows from recent data on large-scale temperature fluctuations $\Delta T/T$ of the cosmic microwave background that either the minimal size of the torus is at least of the…
It is quite remarkable that seventy years after Hubble discovered the expansion of the Universe, we still have no idea in which of the three Friedmann-Robertson-Walker geometries we live. Most of the current literature has focussed on flat…
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…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
If the Universe satisfies a perturbed Friedmann-Lema\^{\i}tre model, then the bright matter (e.g. radio-loud active galactic nuclei, RLAGNs) may be topologically lensed by global geometry. The generation of candidate topological lensing…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
The Hilbert-Einstein equations are insufficient to describe the geometry of the Universe, as they only constrain a local geometrical property: curvature. A global knowledge of the geometry of space, if possible, would require measurement of…
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
The structure formation in the local Universe is considered within the weak-field modification of General Relativity involving the cosmological constant. This approach enables to describe the dynamics of groups and clusters of galaxies, to…
A topologically finite universe, smaller than the observable horizon, will have circles-in-the-sky: pairs of circles around which the temperature fluctuations in the cosmic microwave background are correlated. The circles occur along the…
We qualitatively study the effects of gravitational microlensing on our view of unresolved extragalactic star formation regions. Using a general gravitational microlensing configuration, we perform a number of simulations that reveal that…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…