Geometric and Topological Models of Dark Matter and Dark Energy

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Cosmology".

Deadline for manuscript submissions: closed (10 September 2022) | Viewed by 4605

Special Issue Editors


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Guest Editor
German Aerospace Center (DLR), 10178 Berlin, Germany
Interests: quantum gravity; differential topology of spacetime; cosmology; dark energy and matter; foundation of quantum field theory; quantum geometry
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Guest Editor
Cognitive Science and Mathematical Modelling Chair, University of Information Technology and Management, ul. Sucharskiego 2, 35-225 Rzeszow, Poland
Interests: general relativity; category theory; curvature; synthetic differential geometry; formal set theory methods in smooth manifolds and space-time; space-time singularity

Special Issue Information

Dear Colleagues,

The appearance of large-scale cosmic structures (e.g., the distribution of galaxies) is very hard to understand, particularly in light of the relatively smooth microwave background as measured by the satellites COBE, WMAP, and Planck. One way to accommodate this is to go to a dark matter model in which you have cold dark matter to act as a seed for galaxy formation. One further great mystery in modern cosmology is the accelerated expansion of the universe as driven by dark energy.

Today, dark energy and dark matter are part of the standard model in cosmology. The nature of dark matter and dark energy is currently a hot topic. However, what is known experimentally? Dark matter was never detected in any experiments, but its impact can be observed by gravitational lensing. Current experiments favour the concept of a cosmological constant for dark energy.

Most models of dark matter are related to particle physics, such as axions, sterile neutrinos, etc. Similar ideas such as timely varying scalar fields, known as quintessence, should represent dark energy. However, experimentally, no dark matter particle has been detected and no sign for quintessence has been found. Therefore, why not consider new ideas?

We wish to invite both original and review papers to this Special Issue that particularly emphasize ideas and problems of frameworks based on geometry and/or topology. We believe that such frameworks have a potential to explain dark matter and dark energy at least partially. We are interested in collecting contributions on a broad range of approaches and ideas that emphasize the topological nature of dark matter and dark energy.

Dr. Torsten Asselmeyer-Maluga
Dr. Jerzy Król
Guest Editors

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Published Papers (2 papers)

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Research

15 pages, 427 KiB  
Article
Metrics on End-Periodic Manifolds as Models for Dark Matter
by Christopher L. Duston
Universe 2022, 8(3), 167; https://doi.org/10.3390/universe8030167 - 8 Mar 2022
Viewed by 1872
Abstract
In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of R4. After an overview of the technique, we will present two [...] Read more.
In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of R4. After an overview of the technique, we will present two specific examples, discuss the associated matter models by solving the Einstein equations, and determine the physical viability by examining the energy conditions. We compare the resulting model directly with existing models of matter distributions in extragalactic systems, to highlight the viability of utilizing exotic smooth structures to understand the existence and distribution of dark matter. Full article
(This article belongs to the Special Issue Geometric and Topological Models of Dark Matter and Dark Energy)
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13 pages, 268 KiB  
Article
Dark Matter as Gravitational Solitons in the Weak Field Limit
by Torsten Asselmeyer-Maluga and Jerzy Król
Universe 2020, 6(12), 234; https://doi.org/10.3390/universe6120234 - 9 Dec 2020
Cited by 3 | Viewed by 1806
Abstract
In this paper, we will describe the idea that dark matter partly consists of gravitational solitons (gravisolitons). The corresponding solution is valid for weak gravitational fields (weak field limit) with respect to a background metric. The stability of this soliton is connected with [...] Read more.
In this paper, we will describe the idea that dark matter partly consists of gravitational solitons (gravisolitons). The corresponding solution is valid for weak gravitational fields (weak field limit) with respect to a background metric. The stability of this soliton is connected with the existence of a special foliation and amazingly with the smoothness properties of spacetime. Gravisolitons have many properties of dark matter, such as no interaction with light but act on matter via gravitation. In this paper, we showed that the gravitational lensing effect of gravisolitons agreed with the lensing effect of usual matter. Furthermore, we obtained the same equation of state w=0 as matter. Full article
(This article belongs to the Special Issue Geometric and Topological Models of Dark Matter and Dark Energy)
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