In a newly published study in Astrophysical Journal Letters, researchers used what they said are the largest-ever samples of special galaxies called Lyman-alpha emitters to study how galaxies clumped together over billions of years. In doing so, they gained an improved understanding of how galaxies relate to the surrounding dark matter and how they evolve over time.

“Analyzing these fingerprints gives us insight into the mass of dark matter surrounding the galaxies,” said Eric Gawiser, a Distinguished Professor with the Department of Physics and Astronomy in the Rutgers School of Arts and Sciences and an author of the study. “The dark matter masses revealed by this study are consistent with the idea that Lyman-alpha emitting galaxies evolved into present-day galaxies like our own Milky Way.”

The analysis, which assessed wide-field images across three different eras of the universe’s history shortly after the Big Bang, revealed distinct patterns, akin to cosmic fingerprints. These patterns point to where dark matter is most concentrated, the researchers said.

Dark matter, a mysterious substance that doesn’t emit light or energy, cannot be seen, but makes up most of the matter in the universe, according to scientists. They know dark matter exists because its gravity affects how galaxies move and how these vast cosmic systems are arranged in space.

The study, led by Rutgers doctoral student Dani Herrera, used data from the ODIN (One-hundred-square-degree DECam Imaging in Narrowbands) survey, which is a large astronomical project designed to analyze more than 100,000 Lyman-alpha emitting galaxies.

The researchers focused on data taken from a region of the sky known as the Cosmic Evolution Survey Deep Field (COSMOS), in one of the largest deep-sky surveys ever conducted. Looking deep into space and into the distant past, they viewed three time periods, some 2.8 billion, 2.1 billion and 1.4 billion years after the Big Bang. During these periods, Lyman-alpha emitter galaxies were young and actively forming stars, making them ideal markers for study. They also contain hydrogen gas that emits a special glow, which allows scientists to discover large numbers of them in the distant universe.

“We wanted to find the dark matter whose gravity drives galaxies to merge and grow,” Herrera said. “Understanding where it is and how it has evolved helps us understand how the universe itself has evolved.”

Dark matter plays a crucial role in galaxy formation by acting as a gravitational “glue” that helps pull gas together to form galaxies, Herrera said. Its invisible mass creates deep wells in space where galaxies can grow, merge and evolve, forming the large-scale structure of the universe.

“We used the clumpiness of these galaxies to identify where the dark matter was densest,” Gawiser said. “Visualizing that with a contour map, much the way that a hiking map shows elevations, lets us observe the ‘fingerprints’ of dark matter in the distant universe.”

One result stood out. Three percent to 7% of the dense regions of dark matter capable of hosting galaxies contain Lyman-alpha emitting galaxies, they found. This means that Lyman-alpha emitting galaxies represent a small percentage of the galaxies forming where the dark matter is densest. The low percentage hints that the galaxies were observed during a short-lived phase, glowing in Lyman-alpha light for tens to hundreds of millions of years.

To uncover these results, the researchers used a technique called clustering which measures how galaxies are grouped compared with random distributions. They calculated the angular correlation function, a method of counting pairs of galaxies.

This research, the scientists said, not only deepens understanding of galaxy evolution but also helps scientists refine models of the universe’s structure. As the ODIN survey continues, future studies will expand to more galaxies, offering a more complete view of the cosmic web, they said.

“While invisible to our telescopes, dark matter shapes the universe through interactions with visible material,” Gawiser said. “While some try to understand what it is, others like this research team try to understand where it is and what that implies about the evolution of the universe.”

If that gives you vertigo and you’re wondering how one can understand or even “see” something so vast, the answer is: it isn’t easy. Scientists combine the physics of the Universe with data from astronomical instruments and build theoretical models, such as EFTofLSS (Effective Field Theory of Large-Scale Structure). Fed with observations, these models describe the “cosmic web” statistically and allow its key parameters to be estimated.

Models like EFTofLSS, however, demand a lot of time and computing resources. Since the astronomical datasets at our disposal are growing exponentially, we need ways to lighten the analysis without losing precision. This is why emulators exist: they “imitate” how the models respond, but operate much faster.

Since this is a kind of “shortcut,” what’s the risk of losing accuracy? An international team including, among others, INAF (Italy), The University of Parma (Italy) and the University of Waterloo (Canada) has published in the Journal of Cosmology and Astroparticle Physics (JCAP) a study testing the emulator Effort.jl, which they designed. It shows that Effort.jl delivers essentially the same correctness as the model it imitates — sometimes even finer detail — while running in minutes on a standard laptop instead of a supercomputer.

“Imagine wanting to study the contents of a glass of water at the level of its microscopic components, the individual atoms, or even smaller: in theory you can. But if we wanted to describe in detail what happens when the water moves, the explosive growth of the required calculations makes it practically impossible,” explains Marco Bonici, a researcher at the University of Waterloo and first author of the study. “However, you can encode certain properties at the microscopic level and see their effect at the macroscopic level, namely the movement of the fluid in the glass. This is what an effective field theory does, that is, a model like EFTofLSS, where the water in my example is the Universe on very large scales and the microscopic components are small-scale physical processes.”

The theoretical model statistically explains the structure that gives rise to the data collected: the astronomical observations are fed to the code, which computes a “prediction.” But this requires time and substantial compute. Given today’s data volume — and what is expected from surveys just begun or coming soon (such as DESI, which has already released its first batch of data, and Euclid) — it’s not practical to do this exhaustively every time.

“This is why we now turn to emulators like ours, which can drastically cut time and resources,” Bonici continues. An emulator essentially mimics what the model does: its core is a neural network that learns to associate the input parameters with the model’s already-computed predictions. The network is trained on the model’s outputs and, after training, can generalize to combinations of parameters it hasn’t seen. The emulator doesn’t “understand” the physics itself: it knows the theoretical model’s responses very well and can anticipate what it would output for a new input. Effort.jl’s originality is that it further reduces the training phase by building into the algorithm knowledge we already have about how predictions change when parameters change: instead of making the network “re-learn” these, it uses them from the start. Effort.jl also uses gradients — i.e., “how much and in which direction” predictions change if you tweak a parameter by a tiny amount — another element that helps the emulator learn from far fewer examples, cutting compute needs and allowing it to run on smaller machines.

A tool like this needs extensive validation: if the emulator doesn’t know the physics, how sure are we that its shortcut yields correct answers (i.e., the same ones the model would give)? The newly published study answers exactly this, showing that Effort.jl’s accuracy — on both simulated and real data — is in close agreement with the model. “And in some cases, where with the model you have to trim part of the analysis to speed things up, with Effort.jl we were able to include those missing pieces as well,” Bonici concludes. Effort.jl thus emerges as a valuable ally for analyzing upcoming data releases from experiments like DESI and Euclid, which promise to greatly deepen our knowledge of the Universe on large scales.

The study “Effort.jl: a fast and differentiable emulator for the Effective Field Theory of the Large Scale Structure of the Universe” by Marco Bonici, Guido D’Amico, Julien Bel and Carmelita Carbone is available in the Journal of Cosmology and Astroparticle Physics (JCAP).