Related papers: Cosmic Topology
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…
This work applies the principles of quantum cosmology to examine models incorporating a quintom field. Specifically, three distinct models are analyzed: a simplified toy model, a model featuring an exponential quintom potential, and one…
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…
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to…
Multifield models, arising from multiple scalars interacting with gravity, provide a rich theoretical framework for addressing fundamental problems in modern cosmology. A key role in this regard is played by the so called rapid turn regime,…
A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected first countable space is the image of a nonseparably connected complete metric space…
Recently it has been shown that the cosmological dynamics of covariant $f(Q)$ gravity depend on different affine connections. In this paper, two specific $f(Q)$ models are investigated with SNe+CC+BAO+QSO observational data, and the spatial…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
Topological defects are ubiquitous in condensed-matter physics but only hypothetical in the early universe. In spite of this, even an indirect evidence for one of these cosmic objects would revolutionize our vision of the cosmos. We give…
We assume that the Universe has a non trivial topology whose compact spatial sections have a volume significantly smaller than the horizon volume. By a topological lens effect, such a "folded" space configuration generates multiple images…
The cosmological many-body problem is effectively an infinite system of gravitationally interacting masses in an expanding universe. Despite the interactions' long-range nature, an analytical theory of statistical mechanics describes the…
In this paper we will discuss how cosmic strings can be used to bridge the gap between the local geometry of our spacetime model and the global topology. The primary tool is the theory of foliations and surfaces, and together with…
The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…