  The properties of geodesics flow are studied in a Friedmann-Robertson-Walker
metric perturbed due to the inhomogeneities of matter. The basic, averaged
Jacobi equation is derived, which reveals that the low density regions (voids)
are able to induce hyperbolicity, even if the global curvature of the Universe
is zero or slightly positive. It is shown that the energy independence is a
characteristic property of these geometric effects. The importance of these
conclusions is determined by the temperature independent ellipticity of
excursion sets and regions of different randomness found in Kolmogorov CMB
maps.
