Marked statistics across the cosmic web: Environmental dependent clustering in modified gravity simulations

Imagine the universe as a giant, invisible web stretching across the cosmos, holding everything together. For decades, scientists have believed this web is woven by a set of rules called General Relativity, which explains how gravity works like a gentle, invisible hand pulling matter together. But recently, some clues suggest the universe is expanding faster than these old rules predict, as if there's an invisible "dark energy" pushing it apart. To solve this mystery, some scientists wonder: what if the rules of gravity themselves change when things get very big or very empty? This is the world of "modified gravity," where gravity might get a little stronger in empty spaces, acting like a hidden fifth force that only shows up when the cosmic neighborhood is quiet.

To test this, researchers don't just look at the stars; they look at the shape of the universe itself. They divide the cosmic web into four distinct neighborhoods: Nodes (the busy city centers where galaxy clusters live), Filaments (the long, stringy highways connecting the cities), Walls (the vast, flat sheets of matter), and Voids (the huge, empty deserts between everything). The big question is: if gravity does have a secret fifth force, where would we see it acting up? Would it be in the crowded cities, or would it be whispering loudest in the empty deserts?

This paper takes a deep dive into that question using a giant computer simulation of the universe. The authors, Joaquin Armijo and Lucas Da Costa, created a digital universe that follows the rules of a specific modified gravity theory (called Hu-Sawicki $f(R)$) and compared it to a standard universe governed by normal gravity. They didn't just count galaxies; they used a clever statistical tool called a "marked correlation function." Think of this tool as a way to weigh every pair of galaxies based on their local environment. It's like asking, "Do two galaxies that live in a dense city cluster behave differently than two galaxies living in a lonely void?"

The team found that the modified gravity theory leaves a very specific fingerprint. In their simulation, the "fifth force" makes gravity stronger in low-density areas, causing structures to form differently than in the standard model. However, the most surprising discovery wasn't that the empty voids were the only place to look. While the paper confirms that voids dominate the signal at very large (linear) scales, the study reveals that in the complex, non-linear regime where structures are actively forming, the filaments (the cosmic highways) and the nodes (the city centers) actually hold the most information about this new force. When the researchers combined the data from these two specific environments, they found that the signal for modified gravity became more than four times stronger than if they had just looked at all the galaxies mixed together.

While the voids did show some changes, the study suggests that the real "smoking gun" for detecting these gravity tweaks in the non-linear regime lies in the busy, interconnected parts of the web. The authors simulated this using a box of space 1536 Mpc $h^{-1}$ wide, containing 2048$^3$ particles, and tested it against galaxy samples similar to real-world surveys like CMASS and DESI. They found that for a survey like DESI, looking specifically at the combination of filaments and nodes could boost the ability to spot these gravity deviations by a factor of four compared to current methods.

So, what does this mean for the future? It suggests that if we want to catch gravity breaking the rules, we shouldn't just stare into the empty voids or ignore the busy clusters. We need to pay closer attention to the cosmic highways and the bustling clusters where galaxies hang out, especially when analyzing the complex, non-linear parts of the web. By treating these different neighborhoods as separate clues rather than one big jumble, scientists might finally be able to tell if our understanding of gravity is complete, or if there's a hidden fifth force waiting to be discovered in the strings of the cosmic web.