Geodesic
Similarity of cosmological models and its application to the analysis of cosmological evolution
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 181-198
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Scale transformations of cosmological models based on a statistical system of degenerate fermions with a scalar Higgs interaction are studied. The similarity properties of cosmological models under scale transformations of their fundamental parameters are revealed. The transformation laws for the coordinates of singular points and eigenvalues of the characteristic matrix of the dynamical system of the cosmological model under its scale transformations are established. With the help of the transformation to new variables, the previously studied dynamical system of scalar-charged fermions is modified to a dynamical system with a nondegenerate characteristic matrix; for its nondegenerate branch, the singular points and eigenvalues of the characteristic matrix are found, which coincide with the corresponding values for the vacuum field model. Examples of numerical simulation of such cosmological models are given.
Keywords: scalar-charged plasma, cosmological model, Higgs scalar field, similarity transformation, qualitative analysis. 
@article{TMF_2024_219_1_a11,
     author = {Yu. G. Ignat'ev},
     title = {Similarity of cosmological models and its application to the~analysis of cosmological evolution},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {181--198},
     year = {2024},
     volume = {219},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a11/}
}
TY  - JOUR
AU  - Yu. G. Ignat'ev
TI  - Similarity of cosmological models and its application to the analysis of cosmological evolution
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 181
EP  - 198
VL  - 219
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a11/
LA  - ru
ID  - TMF_2024_219_1_a11
ER  - 
%0 Journal Article
%A Yu. G. Ignat'ev
%T Similarity of cosmological models and its application to the analysis of cosmological evolution
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 181-198
%V 219
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a11/
%G ru
%F TMF_2024_219_1_a11
Yu. G. Ignat'ev. Similarity of cosmological models and its application to the analysis of cosmological evolution. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 181-198. http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a11/

[1] S. Dzh. Klain, Podobie i priblizhennye metody, Mir, M., 1968

[2] L. I. Sedov, Metody podobiya i razmernosti v mekhanike, Nauka, M., 1987 | DOI | MR | Zbl

[3] E. A. Dibai, S. A. Kaplan, Razmernosti i podobie astrofizicheskikh velichin, Nauka, M., 1976

[4] Yu. G. Ignatev, D. Yu. Ignatev, “Kosmologicheskie modeli na osnove statisticheskoi sistemy skalyarno zaryazhennykh vyrozhdennykh fermionov i asimmetrichnogo skalyarnogo dubleta Khiggsa”, TMF, 209:1 (2021), 142–183, arXiv: 2111.00492 | DOI | DOI | MR

[5] G. E. Tauber, J. W. Weinberg, “Internal state of a gravitating gas”, Phys. Rev., 122:4 (1961), 1342–1365 | DOI | MR

[6] Yu. G. Ignat'ev, A. A. Agathonov, D. Yu. Ignatyev, “Cosmological evolution of a statistical system of degenerate scalarly charged fermions with an asymmetric scalar doublet. II. One-component system of doubly charged fermions”, Gravit. Cosmol., 28:1 (2022), 10–24, arXiv: 2203.12766 | DOI | MR

[7] Yu. G. Ignat'ev, “Two-field model of gravitational-scalar instability and formation of supermassive black holes in the early universe”, Gravit. Cosmol., 28:2 (2023), 163–176, arXiv: 2305.15456 | DOI | MR

[8] Yu. G. Ignatev, “Evolyutsiya sfericheskikh vozmuschenii v kosmologicheskoi srede vyrozhdennykh skalyarno zaryazhennykh fermionov so skalyarnym vzaimodeistviem Khiggsa”, TMF, 215:3 (2023), 465–499, arXiv: 2306.17185 | DOI | DOI | MR

[9] B. Saha, G. N. Shikin, “Interacting spinar and scalar fields in Bianchi type I universe filled with perfect fluid: exact self-consistent solutions”, Gen. Rel. Grav., 29:9 (1997), 1099–1113 | DOI | MR

[10] B. Saha, “Spinor field in Bianchi type-I universe: Regular solutions”, Phys. Rev. D, 64:12 (2001), 123501, 15 pp. | DOI | MR

[11] L. P. Chimento, F. P. Devecchi, M. Forte, G. M. Kremer, “Phantom cosmologies and fermions”, Class. Quantum Grav., 25:8 (2008), 085007, 10 pp., arXiv: 0707.4455 | DOI | MR

[12] M. O. Ribas, F. P. Devecchi, G. M. Kremer, “Cosmological model with non-minimally coupled fermionic field”, Europhys. Lett., 81:1 (2008), 19001, 6 pp., arXiv: 0710.5155 | DOI | MR

[13] J. Wang, S.-W. Cui, C.-M. Zhang, “Thermodynamics of spinor quintom”, Phys. Lett. B, 683:2–3 (2010), 101–107, arXiv: 0806.3890 | DOI | MR

[14] L. Fabbri, “Conformal gravity with the most general ELKO matter”, Phys. Rev. D, 85:4 (2012), 047502, 5 pp., arXiv: 1101.2566 | DOI

[15] B. Saha, “Nonlinear spinor fields in Bianchi type-I spacetime: problems and possibilities”, Astrophys. Space Sci., 357:1 (2015), 28, 16 pp., arXiv: 1409.4993 | DOI

[16] K. A. Bronnikov, Yu. P. Rybakov, B. Saha, “Spinor fields in spherical symmetry: Einstein–Dirac and other space-times”, Eur. Phys. J. Plus, 135:1 (2020), 124, 10 pp., arXiv: 1909.04789 | DOI

[17] O. I. Bogoyavlenskii, Metody kachestvennoi teorii dinamicheskikh sistem v astrofizike i gazovoi dinamike, Nauka, M., 1980 | MR | Zbl

[18] Yu. G. Ignatev, I. A. Kokh, “Polnaya kosmologicheskaya model na osnove asimmetrichnogo skalyarnogo dubleta Khiggsa”, TMF, 207:1 (2021), 133–176, arXiv: 2104.01054 | DOI | DOI | MR

[19] Yu. G. Ignat'ev, “Formation of supermassive nuclei of black holes in the early universe by the mechanism of scalar-gravitational instability. I. Local picture”, Gravit. Cosmol., 29:4 (2023), 327–344, arXiv: 2308.03192 | DOI | MR

[20] G. Leon, A. Paliathanasis, J. L. Morales, “The past and future dynamics of quintom dark energy models”, Eur. Phys. J C, 78 (2018), 753, 22 pp., arXiv: 1808.05634 | DOI