Abstract:
A mathematical model is constructed for the evolution of spherical perturbations in a cosmological one-component statistical system of completely degenerate scalar-charged fermions with a scalar Higgs coupling. A complete system of self-consistent equations for the evolution of small spherical perturbations is constructed. Singular parts in perturbation modes corresponding to a point-like mass and scalar charge are singled out. We obtain systems of ordinary differential equations for the evolution of the mass and charge of a singular source and systems of partial differential equations for the evolution of nonsingular parts of perturbations. The coefficients of partial differential equations are described by solutions of evolutionary equations for mass and charge. The problem of spatially localized perturbations for solutions that are polynomial in the radial coordinate is reduced to a recurrent system of ordinary linear differential equations for the coefficients of these polynomials. The properties of solutions are studied in the case of cubic polynomials; in particular, it is shown that the radii of localization of gravitational and scalar perturbations coincide and evolve in proportion to the scale factor. The evolution of perturbations is modeled numerically, which in particular confirms the exponential growth of the central mass of the perturbation, and also reveals the oscillatory nature of the evolution of the scalar charge.
The work was carried out at the expense of a subsidy allocated as part of the state support of the Kazan (Volga
Region) Federal University in order to increase its competitiveness
among the world's leading scientific and educational centers.
Citation:
Yu. G. Ignatev, “Evolution of spherical perturbations in the cosmological
environment of degenerate scalar-charged fermions with a scalar
Higgs coupling”, TMF, 215:3 (2023), 465–499; Theoret. and Math. Phys., 215:3 (2023), 862–892
\Bibitem{Ign23}
\by Yu.~G.~Ignatev
\paper Evolution of spherical perturbations in the~cosmological
environment of degenerate scalar-charged fermions with a~scalar
Higgs coupling
\jour TMF
\yr 2023
\vol 215
\issue 3
\pages 465--499
\mathnet{http://mi.mathnet.ru/tmf10348}
\crossref{https://doi.org/10.4213/tmf10348}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4602497}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...215..862I}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 215
\issue 3
\pages 862--892
\crossref{https://doi.org/10.1134/S0040577923060089}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85162897942}
Linking options:
https://www.mathnet.ru/eng/tmf10348
https://doi.org/10.4213/tmf10348
https://www.mathnet.ru/eng/tmf/v215/i3/p465
This publication is cited in the following 9 articles:
Yu. G. Ignatev, “Evolution of plane perturbations in the cosmological environment of the Higgs scalar field and an ideal scalar-charged fluid”, Theoret. and Math. Phys., 222:2 (2025), 285–313
Yu. G. Ignat'ev, A. R. Samigullina, “Cosmological Models Based on an Asymmetric Scalar Higgs Doublet with Potential Interactions between Components”, Gravit. Cosmol., 31:1 (2025), 1
Yu. G. Ignatev, “Evolyutsiya sfericheskikh vozmuschenii v kosmologicheskoi srede khiggsova skalyarnogo polya i idealnoi skalyarno zaryazhennoi zhidkosti”, TMF, 223:1 (2025), 127–142
Yu. G. Ignat'ev, “Evolution of spherical perturbations in the cosmological environment of the Higgs scalar field and an ideal scalar charged fluid”, Theoret. and Math. Phys., 223:1 (2025), 636–649
Yu. G. Ignat'ev, “Similarity of cosmological models and its application to the analysis of cosmological evolution”, Theoret. and Math. Phys., 219:1 (2024), 688–703
Yu. G. Ignat'ev, “Formation of Supermassive Nuclei of Black Holes in the Early Universe by the Mechanism of Scalar-Gravitational Instability. II. Evolution of Localized Spherical Perturbations1”, Gravit. Cosmol., 30:1 (2024), 40
Yu. G. Ignat'ev, “Self-gravitating Higgs field of an asymmetric binary scalar charge”, Theoret. and Math. Phys., 221:1 (2024), 1711–1725
Yu. G. Ignat'ev, I. A. Kokh, “Cosmological Models Based on an Asymmetric Scalar Doublet with Kinetic Coupling of Components. II. Numerical Modeling”, Gravit. Cosmol., 30:4 (2024), 426
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 1”, Gravit. Cosmol., 29:4 (2023), 327
Citation in format AMSBIB
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