Mathematical Cosmology

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 4291

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Mathematics Department, US Naval Academy, Annapolis, MD 21402, USA
Interests: mathematical physics; general relativity; singularities; exact solutions
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Special Issue Information

Dear Colleagues,

Mathematical cosmology is the study of the construction, the structure, and the intrinsic content of an exact cosmological spacetime within Einsteinian gravity or an alternate classical theory. A cosmological spacetime is usually a manifold and a metric together with a fundamental time-like vector field; however, chaotic, topologically nontrivial, non-Hausdorff, and even acausal models do arise and are considered. Furthermore, purely mathematical questions like those pertaining to genericity and stability of the models and their intrinsic features (e.g., singularities, horizons, topological defects, etc.) arise in both classical and quantum-related theories, theories such as string theory and loop quantum gravity.

This Special Issue is a place to share your mathematical work on cosmological spacetimes and their intrinsic global features. Studies of new exact solutions in Einstein gravity or alternative theories are welcome as well as quantum extensions such as string cosmology and loop cosmology. Physically interesting analyses of the structure and features of cosmological spacetimes is also welcome. In particular, studies of the rarer types of global features such as the mild quasiregular and non-scalar curvature singularities or unusual cosmological milestones such as sudden singularities or big rips would also appropriate. Finally, any mathematical analyses that may shed light on the genericness or stability of these cosmological spacetimes is welcome.

Prof. Dr. Deborah Konkowski
Guest Editor

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Published Papers (4 papers)

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Research

43 pages, 596 KiB  
Article
Emergent Spacetime and Cosmic Inflation
by Hyun Seok Yang
Universe 2024, 10(3), 150; https://doi.org/10.3390/universe10030150 - 21 Mar 2024
Cited by 13 | Viewed by 971
Abstract
We present a novel background-independent framework for cosmic inflation, starting with a matrix model. In this framework, inflation is portrayed as a dynamic process responsible for the generation of both space and time. This stands in contrast to conventional inflation, which is characterized [...] Read more.
We present a novel background-independent framework for cosmic inflation, starting with a matrix model. In this framework, inflation is portrayed as a dynamic process responsible for the generation of both space and time. This stands in contrast to conventional inflation, which is characterized as a mere (exponential) expansion of an already existing spacetime, driven by the vacuum energy associated with an inflaton field. We observe that the cosmic inflation is triggered by the condensate of Planck energy into a vacuum and responsible for the dynamical emergence of spacetime. The emergent spacetime picture admits a background-independent formulation so that the inflation is described by a conformal Hamiltonian system which requires neither an inflaton field nor an ad hoc inflation potential. This implies that the emergent spacetime may incapacitate all the rationales to introduce the multiverse hypothesis. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
14 pages, 332 KiB  
Article
Teleparallel Robertson-Walker Geometries and Applications
by Alan Albert Coley, Alexandre Landry and Fateme Gholami
Universe 2023, 9(10), 454; https://doi.org/10.3390/universe9100454 - 21 Oct 2023
Cited by 1 | Viewed by 1063
Abstract
In teleparallel geometries, the coframe and corresponding spin connection are the principal geometric objects and, consequently, the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six [...] Read more.
In teleparallel geometries, the coframe and corresponding spin connection are the principal geometric objects and, consequently, the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six dimensional Lie algebra of Robertson–Walker affine symmetries are displayed and discussed. We will refer to such geometries as teleparallel Robertson–Walker (TRW) geometries, where the corresponding derived metric is of Robertson–Walker form and is characterized by the parameter k=(1,0,1). The field equations are explicitly presented for the F(T) class of teleparallel TRW spacetimes. We are primarily interested in investigating the k0 TRW models. After first studying the k=0 models and, in particular, writing their governing field equations in an appropriate form, we then study their late time stability with respect to perturbations in k in both the cases of a vanishing and non-vanishing effective cosmological constant term. As an illustration, we consider both quadratic F(T) theories and power-law solutions. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
27 pages, 407 KiB  
Article
Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame
by Alexandre Landry and Robert J. van den Hoogen
Universe 2023, 9(5), 232; https://doi.org/10.3390/universe9050232 - 15 May 2023
Cited by 1 | Viewed by 784
Abstract
A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation [...] Read more.
A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation scheme can be transformed to one in which perturbations all take place within the co-frame. A covariant definition of a teleparallel Minkowski geometry is proposed. We compute the perturbed field equations for f(T) teleparallel gravity and discuss the stability of the teleparallel Minkowski geometry within f(T) teleparallel gravity. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
17 pages, 950 KiB  
Article
Traveling Wave Solutions and Conservation Laws of a Generalized Chaffee–Infante Equation in (1+3) Dimensions
by Motshidisi Charity Sebogodi, Ben Muatjetjeja and Abdullahi Rashid Adem
Universe 2023, 9(5), 224; https://doi.org/10.3390/universe9050224 - 08 May 2023
Cited by 4 | Viewed by 929
Abstract
This paper aims to analyze a generalized Chaffee–Infante equation with power-law nonlinearity in (1+3) dimensions. Ansatz methods are utilized to provide topological and non-topological soliton solutions. Soliton solutions to nonlinear evolution equations have several practical applications, including plasma physics and the diffusion process, [...] Read more.
This paper aims to analyze a generalized Chaffee–Infante equation with power-law nonlinearity in (1+3) dimensions. Ansatz methods are utilized to provide topological and non-topological soliton solutions. Soliton solutions to nonlinear evolution equations have several practical applications, including plasma physics and the diffusion process, which is why they are becoming important. Additionally, it is shown that for certain values of the parameters, the power-law nonlinearity Chaffee–Infante equation allows solitons solutions. The requirements and restrictions for soliton solutions are also mentioned. Conservation laws are derived for the aforementioned equation. In order to comprehend the dynamics of the underlying model, we graphically show the secured findings. Hirota’s perturbation method is included in the multiple exp-function technique that results in multiple wave solutions that contain new general wave frequencies and phase shifts. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
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