On de-Sitter Geometry in Cosmic Void Statistics

Abstract

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.

8 pages, 4 figures, accepted by MNRAS. Minor changes, appendix added

References in corpus (5)

• The Measure Problem in Cosmology
• Excursion Sets and Non-Gaussian Void Statistics
• Fractal Dimensions of a Weakly Clustered Distribution and the Scale of Homogeneity
• Halos and voids in a multifractal model of cosmic structure
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• Lie sphere-geometry in lattice cosmology
• Analysis of Cosmological Generalized Reduced Void Probability Functions Constrained by Observations and Numerical Simulations
• Cosmic voids and BAO with relative baryon-CDM perturbations