Poisson clusters and Poisson voids

Mathematics – Probability

Scientific paper

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Cosmology, Galactic Clusters, Neutrinos, Poisson Density Functions, Probability Theory, Voids, Monte Carlo Method, Random Processes

Scientific paper

The probabilites of the occurrence of clusters of celestial objects or voids are calculated to examine the likelihood that observed heavy source regions of neutrinos are or are not evidence for a large scale structure in the universe. The probabilities are treated in terms of expected abundances of the clusters or voids in a unit volume of space represented by three-dimensional spheres. It is shown that calculated abundances will depend on the shape chosen for the trial volume. The investigation is therefore extended to consider circles and squares (and ellipses and rectangles). When applied to a region of the sky known to contain no Abell clusters, the observed voids are found to be accounted for by random fluctuations. The lack of uniqueness of the voids is observed whether circular or square regions are evaluated.

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