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Axioms
Special Issues
Mathematical Cosmology
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Mathematical Cosmology

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 7269

Special Issue Editors

Prof. Dr. Irina Radinschi

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Guest Editor
Department of Physics, “Gheorghe Asachi” Technical University, 700050 Iasi, Romania
Interests: general relativity and cosmology; computational physics; string theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Saibal Ray

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Guest Editor
Centre for Cosmology, Astrophysics and Space Science (CCASS) GLA University, 17th KM Mile Stone, NH-2, Mathura-Delhi Highway Road, P.O. Chaumuhan, Mathura 281406, Uttar Pradesh, India
Interests: general relativity; stellar astrophysics; brane-world model and galactic dynamics; dark energy theory; cosmic expansion
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Prof. Dr. Farook Rahaman

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Guest Editor
Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India
Interests: mathematical physics; relativity; cosmology and astrophysics
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Dr. Theophanes Grammenos

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Guest Editor
Department of Civil Engineering, University of Thessaly, 383 34 Volos, Greece
Interests: mathematical physics; general relativity; differential geometry; differential equations
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Dr. Marius Mihai Cazacu

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Guest Editor
Department of Physics, Gheorghe Asachi Technical University of Lași, 700050 Lași, Romania
Interests: atmospheric aerosol measurements; atmosphere; pollution; remote sensing; optics and spectroscopy; laser; physics; applied science; environmental engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Cosmology as the study of properties and evolution of the large-scale structure of the Universe has been extremely boosted and expanded by spectacular technological and scientific developments in recent decades. Mathematical cosmology is cosmology with an emphasis on mathematical rigor and the underlying conceptual principles, i.e., mathematical cosmology seeks the relevant mathematical details in order not only to provide a deeper understanding of the existing cosmological models thereby stressing their geometrical and/or topological background but also to motivate the formulation and construction of new theories and models. In this sense, mathematical cosmology, though actually a subject of modern mathematical and theoretical physics, is an independent scientific area that can be considered, by applying classical as well as modern mathematical methods, as a testing ground for bringing forward and illuminating the connection of general relativity with quantum gravity, string theory, and modified theories of gravity, all placed in the arena of theoretical cosmology.

In the aforementioned context, there still remain many unresolved mathematical and theoretical-physical problems that set the tone for recent research. The present Special Issue is aiming at presenting modern solution efforts and attempts in the hope of providing a clearer picture of these questions and their possible answers that frame mathematical cosmology today, thereby expanding our knowledge in this scientific area. In this sense, we welcome original research articles as well as review articles on advances in mathematical and/or theoretical cosmology including the following areas:

  • General-relativistic cosmology
  • Energy-momentum localization in cosmological space-times
  • Singularities in cosmology
  • Scalar field cosmology
  • Scalar-tensor cosmology
  • Hamiltonian cosmology
  • Cosmology and dynamical systems
  • Inhomogeneous and anisotropic cosmology
  • Topological issues in cosmology
  • Cosmology and modified gravity theories
  • Dark cosmology
  • Higher-dimensional cosmology
  • String/Brane cosmology
  • Early universe and inflationary cosmology
  • Quantum cosmology
  • Twistor/spinor cosmology
  • Cosmological magnetogenesis
  • Observational cosmology: data analysis
  • CMBR: computer computation

Prof. Dr. Irina Radinschi
Prof. Dr. Saibal Ray
Prof. Dr. Farook Rahaman
Dr. Theophanes Grammenos
Dr. Marius Mihai Cazacu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (5 papers)

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Research

19 pages, 337 KiB  
Article
Semi-Classical Limit and Quantum Corrections in Non-Coincidence Power-Law f(Q)-Cosmology
by Andronikos Paliathanasis
Axioms 2024, 13(9), 619; https://doi.org/10.3390/axioms13090619 - 11 Sep 2024
Viewed by 430
Abstract
Within the framework of symmetric teleparallel fQ-gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler–DeWitt equation of quantum cosmology. The gravitational field equation in fQ-gravity permits a minisuperspace description, rendering the Wheeler–DeWitt equation a single [...] Read more.
Within the framework of symmetric teleparallel fQ-gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler–DeWitt equation of quantum cosmology. The gravitational field equation in fQ-gravity permits a minisuperspace description, rendering the Wheeler–DeWitt equation a single inhomogeneous partial differential equation. We use the power-law fQ=f0Qμ model, and with the application of linear quantum observables, we calculate the wave function of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
18 pages, 677 KiB  
Article
Mass Generation via the Phase Transition of the Higgs Field
by Dimitris M. Christodoulou and Demosthenes Kazanas
Axioms 2023, 12(12), 1093; https://doi.org/10.3390/axioms12121093 - 29 Nov 2023
Viewed by 1208
Abstract
The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of [...] Read more.
The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is “broken” by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
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15 pages, 1063 KiB  
Article
A Comparison of Hořava–Lifshitz Gravity and Einstein Gravity through the Gravitational Deflection of Massive Body around Black Holes
by Safiqul Islam and Farook Rahaman
Axioms 2023, 12(4), 364; https://doi.org/10.3390/axioms12040364 - 10 Apr 2023
Cited by 1 | Viewed by 1282
Abstract
Hořava has proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions. This theory may be regarded as a UV complete candidate for general relativity. After the proposal of this theory, Kehagias and Sfetsos have found a new asymptotically flat black [...] Read more.
Hořava has proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions. This theory may be regarded as a UV complete candidate for general relativity. After the proposal of this theory, Kehagias and Sfetsos have found a new asymptotically flat black hole solution in Hořava–Lifshitz gravity. In recent times, a new test of gravity theory is suggested that assumes the deflection of the massive body around a black hole. In this paper, we will study the effect of the Hořava–Lifshitz parameters on the black hole deflection angle and emphasize those features that permit a comparison of Hořava–Lifshitz to Einstein gravity. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
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21 pages, 5828 KiB  
Article
Stability of Anisotropy Pressure in Self-Gravitational Systems in f(G) Gravity
by Z. Yousaf, M. Z. Bhatti, S. Khan, A. Malik, Haifa I. Alrebdi and Abdel-Haleem Abdel-Aty
Axioms 2023, 12(3), 257; https://doi.org/10.3390/axioms12030257 - 2 Mar 2023
Cited by 37 | Viewed by 1497
Abstract
This investigation aims to explore certain variables which are considered responsible for generating pressure anisotropy in dynamical spherically symmetric stellar systems against the background of the stringy-inspired Gauss–Bonnet modification of general relativity. We explore the hydrostatic equilibrium of self-gravitating systems by taking into [...] Read more.
This investigation aims to explore certain variables which are considered responsible for generating pressure anisotropy in dynamical spherically symmetric stellar systems against the background of the stringy-inspired Gauss–Bonnet modification of general relativity. We explore the hydrostatic equilibrium of self-gravitating systems by taking into account the modified form of Tolman–Oppenheimer–Volkoff for the quadratic-f(G) gravitational model. In this respect, we formulate a differential equation in terms of the Weyl curvature scalar, also described as an evolution equation, which is essential for understanding the evolution of the stellar structure. Finally, we conclude that the existence of some fluid variables such as shear, heat flux and the irregular behavior of energy density in the presence of an extra degree f(G)-terms in the fluid flow that are the elements that cause anisotropy in the initially isotropic stellar structure. The comparison of the presented results with those of the classical model shows that they are physically relevant and compatible. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
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31 pages, 3847 KiB  
Article
Modified Gravity Description of Neutron Star in the f(R) Framework
by Samprity Das, Irina Radinschi and Surajit Chattopadhyay
Axioms 2023, 12(3), 234; https://doi.org/10.3390/axioms12030234 - 23 Feb 2023
Cited by 6 | Viewed by 1806
Abstract
The present paper reports a study on neutron stars in the f(R) gravity framework for the Hu–Sawicki model, Starobinsky model, Tsujikawa model, and Exponential Gravity model. First, we have used the TOV equation for the f(R) gravity [...] Read more.
The present paper reports a study on neutron stars in the f(R) gravity framework for the Hu–Sawicki model, Starobinsky model, Tsujikawa model, and Exponential Gravity model. First, we have used the TOV equation for the f(R) gravity framework, where we obtained two higher order differential equations for λ and ψ, with both functions depending on the radial coordinate. Furthermore, we have considered the BD theory, which is an equivalent theory of f(R) gravity, and introduced a new scalar field ϕ2 with the scalar potential V(ϕ2). We have observed an increase in the scalar potential with respect to R in each case. Furthermore, our proposed models, namely quadratic form, exponential form, and linear form and the other viable models show a similar type of evolution for the scalar potential V(ϕ2). Full article
(This article belongs to the Special Issue Mathematical Cosmology)
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