On de-Sitter Geometry in Cosmic Void Statistics
  Starting from the geometrical concept of a 4-dimensional de-Sitter
configuration of spheres in Euclidean 3-space and modelling voids in the
Universe as spheres, we show that a uniform distribution over this
configuration space implies a power-law for the void number density which is
consistent with results from the excursion set formalism and with data, for an
intermediate range of void volumes. The scaling dimension of the large scale
structure can be estimated as well. We also discuss the effect of restricting
the survey geometry on the void statistics. This work is a new application of
de-Sitter geometry to cosmology and also provides a new geometrical perspective
on self-similarity in cosmology.
