The Disordered Heterogeneous Universe: Galaxy Distribution and Clustering Across Length Scales

Abstract: Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at microscales' to predict physical properties atmacroscales', whether for a liquid, composite material, or entire Universe. The former theory provides an array of techniques to characterize a wide class of microstructures; in this work, we apply them to the distributions of galaxies. We focus on the lower-order correlation functions, void' andparticle' nearest-neighbor functions, pair-connectedness functions, percolation properties, and a scalar order metric. Compared to homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the nearest-neighbor functions, due to the presence of quasi-long-range correlations. On large scales, the system appears hyperuniform', due to primordial density fluctuations, whilst on the smallest scales, the system becomes almostantihyperuniform', and, via the order metric, is shown to be a highly correlated disordered system. Via a finite scaling analysis, we show that the percolation threshold of the galaxy catalogs is significantly lower than for Poisson realizations; this is consistent with the observation that the galaxy distribution contains larger voids. However, the two sets of simulations share a fractal dimension, implying that they lie in the same universality class. Finally, we consider the ability of large-scale clustering statistics to constrain cosmological parameters using simulation-based inference. Both the nearest-neighbor distribution and pair-connectedness function considerably tighten bounds on the amplitude of cosmological fluctuations at a level equivalent to observing twenty-five times more galaxies. These are a useful alternative to the three-particle correlation, and are computable in much reduced time. (Abridged)