  The degree of randomness in the cosmic microwave background (CMB) maps has
been shown to be measurable and indicative of the hyperbolic effect of voids on
the propagation of the photon beams. In terms of an introduced porosity
parameter, we now obtain the criterion for a hyperbolicity due to domination of
voids in the line-of-sight direction. The criterion seems to be supported by
the parameters of 30 Mpc scale voids revealed by the galactic redshift surveys.
The importance of the geometrical effect of the voids is also due to their
possible role in the temperature independent ellipticity of the excursion sets,
as well as in the nature of dark energy. The role of possible larger scale
inhomogeneities, from superclusters to semi-Hubble scale, in this effect
remains yet unclear.
