Void statistics, scaling, and the origins of large-scale structure

The probability that a volume of the universe of given size and shape spaced at random will be void of galaxies is used here to study various models of the origin of cosmological structures. Numerical simulations are conducted on hot-particle and cold-particle-modulated inflationary models with and without biasing, on isothermal or initially Poisson models, and on models where structure is seeded by loops of cosmic string. For the Pisces-Perseus redshift compilation of Giovanelli and Haynes (1985), it is found that hierarchical scaling is obeyed for subsamples constructed with different limiting magnitudes and subsamples taken at random. This result confirms that the hierarchical ansatz holds valid to high order and supports the idea that structure in the observed universe evolves by a regular process from an almost Gaussian primordial state. Neutrino models without biasing show the effect of a strong feature in the initial power spectrum. Cosmic string models do not agree well with the galaxy data.