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

G. A. Alekseev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 281 (2013), pp. 137-148

Résumé

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.