  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.
