Abstract
The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density in our fiducial analysis compared to ), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much larger than the average intergalaxy separation, implying that they lie in the same universality class. We also show that the distribution of galaxies is a highly correlated disordered system (relative to the uncorrelated Poisson distribution), as measured by the order metric. Finally, we consider the ability of large-scale clustering statistics to constrain cosmological parameters, such as the Universe’s expansion rate, using simulation-based inference. Both the nearest-neighbor distribution and pair-connectedness function (which includes contributions from correlation functions of all order) are found to considerably tighten bounds on the amplitude of quantum-mechanical fluctuations from inflation at a level equivalent to observing 25 times more galaxies. The pair-connectedness function in particular provides a useful alternative to the standard three-particle correlation, since it contains similar large-scale information to the three-point function, can be computed highly efficiently, and can be straightforwardly extended to small scales (though likely requires simulation-based modeling). This work provides the first application of such techniques to cosmology, providing both a novel system to test heterogeneous media descriptors and a tranche of new tools for cosmological analyses. A range of extensions are possible, including implementation on observational data; this will require further study on various observational effects, necessitating high-resolution simulations.
6 More- Received 16 July 2022
- Revised 2 January 2023
- Accepted 10 January 2023
DOI:https://doi.org/10.1103/PhysRevX.13.011038
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
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The Cosmos as a Colloid
Published 14 March 2023
A new methodology for analyzing the 3D distribution of galaxies borrows techniques from the study of colloids and other disordered materials.
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Popular Summary
The distribution of galaxies traces the distribution of matter in the early Universe. As such, it encodes information on a wealth of cosmological parameters, such as the density of matter. An open question is how best to analyze the data. Most works focus on measuring the correlation functions of the galaxy distribution and comparing them to physical models, though this is known to be suboptimal. While many alternatives have been proposed, there is little consensus on which have practical utility, and few are natural from a theoretical standpoint. Here, we show that tools from the theory of disordered heterogeneous media are well suited to characterizing the distribution of galaxies and yield new information on the Universe’s structure and evolution.
The galaxy distribution is a unique 3D set of irregularly arranged points. As such, heterogeneous-media and statistical-mechanical techniques designed to quantify the spatial structure and topology of many-particle material microstructures can be used to understand the galaxy distribution. We use several statistical descriptors from the theory of disordered heterogeneous media to characterize galaxy distributions seen in recent dark matter simulations. We find that the new descriptors can constrain cosmological parameters such as the amplitude of early-Universe quantum fluctuations, yielding bounds that are 5 times tighter than those of conventional statistics, with negligible additional computational requirements.
Employing these tools enables us to extract new information from galaxy distributions and offers new challenges to devise even better statistical descriptors. A key next step will be the application to observational data, which will require updated modeling and consideration of all relevant observational effects.