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

TL;DR

This paper presents exact solutions showing how primordial magnetic fields influence the evolution of initially homogeneous and isotropic universes, causing anisotropic expansion and partial space-time closure.

Contribution

It introduces new exact solutions of Einstein-Maxwell equations with magnetic fields affecting universe evolution, under a stiff matter equation of state.

Findings

Magnetic fields induce anisotropic expansion and contraction.

Partial dynamical closure of space-time occurs at large distances.

Solutions are based on a stiff matter equation of state.

Abstract

Simple exact solutions presented here describe the universes which spatial geometries are asymptotically homogeneous and isotropic near the initial singularity, but which evolution goes 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 -- 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 goes with acceleration in spatial directions across the magnetic field, and with deceleration along the magnetic lines, so that in flat and open models, in fluid comoving coordinates, the lengths of $\varphi$-circles of large enough radius or for late enough times decrease and vanish for $t\to\infty$. This means that in flat and open models, we have a partial dynamical closure of space-time at large distances from the 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 for the perfect fluid (which supports the isotropic and homogeneous "background" Friedmann geometries) rather exotic, stiff matter equation of state $\varepsilon=p$. However, it seems reasonable to expect that similar effects might take place in the mutual dynamics of geometry and strong electromagnetic fields in the universes with more realistic matter equations of state.