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 Tr. Mat. Inst. Steklova, 2013, Volume 281, Pages 137–148 (Mi tm3474)

Influence of electromagnetic fields on the evolution of initially homogeneous and isotropic universe

G. A. Alekseev

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: Simple exact solutions presented here describe universes whose spatial geometries are asymptotically homogeneous and isotropic near the initial singularity but whose evolution proceeds under the influence of primordial magnetic fields. In all these “deformed” Friedmann models (spatially flat, open or closed), the initial magnetic fields are concentrated near some axis of symmetry and their lines are the circles given by the lines of the azimuthal coordinate $\varphi$. Caused by the expansion of the universe, the time dependence of a magnetic field induces (in accordance with the Faraday law) the emergence of source-free electric fields. In comparison with the Friedmann models, the cosmological expansion proceeds with acceleration in the spatial directions across the magnetic field and with deceleration along the magnetic lines, so that in the flat and open models, in fluid comoving coordinates, the lengths of $\varphi$-circles of sufficiently large radius or for sufficiently late times decrease and vanish as $t\to\infty$. This means that in the flat and open models we have a partial dynamical closure of space-time at large distances from the symmetry axis, i.e., from the regions where the electromagnetic fields in our solutions are concentrated. To get simple exact solutions of the Einstein–Maxwell and perfect fluid equations, we assume a rather exotic stiff matter equation of state $\varepsilon=p$ for the perfect fluid (which supports isotropic and homogeneous “background” Friedmann geometries). However, it seems reasonable to expect that similar effects might occur in the mutual dynamics of geometry and strong electromagnetic fields in universes with more realistic matter equations of state.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-0003411-01-00440 Russian Academy of Sciences - Federal Agency for Scientific Organizations The author expresses his deep thanks to ICRANet (Pescara, Italy) and to the Institut des Hautes Etudes Scientifiques (Buressur-Yvette, France) for financial support and hospitality during his visits in June and October 2012, respectively, when parts of this work were made. The work was also supported in part by the Russian Foundation for Basic Research (project nos. 11-01-00034 and 11-01-00440) and by the program "Fundamental Problems of Nonlinear Dynamics" of the Russian Academy of Sciences.

DOI: https://doi.org/10.1134/S0371968513020118

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 281, 129–139

Bibliographic databases:

Document Type: Article
UDC: 530.12+531.51+537.8

Citation: G. A. Alekseev, “Influence of electromagnetic fields on the evolution of initially homogeneous and isotropic universe”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 137–148; Proc. Steklov Inst. Math., 281 (2013), 129–139

Citation in format AMSBIB
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• https://doi.org/10.1134/S0371968513020118
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