Porosity criterion for hyperbolic voids and the cosmic microwave   background
  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. 
V. G. Gurzadyan, A. A. Kocharyan