Related papers: The no-defect conjecture in cosmic crystallography
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
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…
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It…
Topological defects are ubiquitous from solid state physics to cosmology, where they drive phase transitions by proliferating as domain walls, monopoles or vortices. As quantum excitations, they often display fractional charge and anyonic…
Recent observations suggest that the ratio of the total density to the critical density of the universe, $\Omega_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with…
The interplay between cosmology and strongly coupled dynamics can yield transient spectral features that vanish at late times, but which may leave behind phenomenological signatures in the spectrum of primordial fluctuations. Of particular…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
We study the behavior of non-relativistic quantum particles interacting with different potentials in the space-times generated by a cosmic string and a global monopole. We find the energy spectra in the presence of these topological defects…
As is well known, black hole entropy is proportional to the area of the horizon suggesting a holographic principle wherein all degrees of freedom contributing to the entropy reside on the surface. In this note, we point out that large scale…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
The topological theory and the Volterra process are key tools for the classification of defects in Condensed Mater Physics. We employ the same methods to classify the 2D defects of a 4D maximally symmetric spacetime. These \textit{cosmic…
This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical…
Models including an energy transfer from CDM to DE are widely considered in the literature, namely to allow DE a significant high-z density. Strongly Coupled cosmologies assume a much larger coupling between DE and CDM, together with the…
Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in…
While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of…
We show that our Universe may be inhomogeneous on large sub-horizon scales without us being able to realise it. We assume that a network of domain walls permeates the universe dividing it in domains with slightly different vacuum energy…
Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…
One signature of an expanding universe is the time-variation of the cosmological abundances of its different components. For example, a radiation-dominated universe inevitably gives way to a matter-dominated universe, and critical moments…