Pinpoint simulations provide insight into the structure of the universe

The universe is dotted with galaxies, which at large scales exhibit a thread pattern called the cosmic web. This heterogeneous distribution of cosmic material is somewhat like blueberries in a muffin, where material may accumulate in certain areas but be absent in others.

Based on a series of simulations, researchers have begun to study the heterogeneous structure of the universe by treating the distribution of galaxies as a collection of points – like the individual particles of matter that make up a material – rather than as a continuous distribution. This technique has enabled the application of the mathematics developed for materials science to quantify the relative disorder of the universe and provide a better understanding of its fundamental structure.

“We found that the distribution of galaxies in the Universe differs significantly from the physical properties of conventional materials and has its own unique signature,” explains Oliver Philcox, a co-author of the study.

This work, now published in Physical Check X, was conducted by Salvatore Torquato, Frequent Fellow and Visitor at the Institute for Advanced Study and Lewis Bernard Professor of Science in the Chemistry and Physics Departments at Princeton University; and Oliver Philcox a visiting Ph.D. Student at the Institute from September 2020 to August 2022, now Junior Fellow in the Simons Society of Fellows, hosted at Columbia University.

The pair analyzed public simulation data generated by Princeton University and the Flatiron Institute. Each of the 1,000 simulations consists of a billion dark matter “particles” whose gravitationally evolved clusters serve as proxies for galaxies.

One of the main results of the work concerns the correlations of pairs of galaxies that are topologically connected by the pair-connectedness function. On this basis – and the range of other descriptors that emerge in heterogeneous media theory – the research team showed that at the largest scales (of the order of several hundred megaparsecs) the universe is approaching hyperuniformity, while at smaller scales (down to to 10 megaparsecs) it becomes almost antihyperuniform and highly inhomogeneous.

“The perceived alternation between order and disorder is largely dependent on magnitude,” Torquato said. “Georges Seurat’s pointillist technique in the painting A Sunday on La Grande Jatte creates a similar visual effect; the work appears disordered up close and very ordered from afar. In relation to the universe, the degree of order and disorder is more subtle, like a Rorschach inkblot test that can be interpreted in an infinite number of ways.

Statistical tools, notably nearest neighbor distributions, clustering diagnostics, Poisson distributions, percolation thresholds, and the pair-connected function, allowed researchers to develop a consistent and objective framework for measuring order. Therefore, although their findings were made in a cosmological context, they can be extrapolated to a range of other dynamic physical systems.

This interdisciplinary work, combining techniques from cosmology and condensed matter physics, has future implications for both fields. In addition to the distribution of galaxies, many other features of the Universe can be explored with these tools, including cosmic voids and the ionized hydrogen bubbles that formed during the reionization phase of the Universe.

Conversely, the novel phenomena discovered about the universe could also provide insights into various material systems on Earth. The team recognizes that more work will be needed before these techniques can be applied to real data, but this work provides a strong proof of concept with significant potential.