To explain away dark matter, gravity would have to be really weird, cosmologists say

The spatial distribution of more than 4 million galaxies as measured by the Sloan Digital Sky Survey, which can’t be easily explained by modifying gravity


Dark matter, the invisible stuff whose gravity is thought to hold galaxies together, may be the least satisfying concept in physics. But if you want to get rid of it, a new study finds, you’ll need to replace it with something even more bizarre: a force of gravity that, at some distances, pulls massive objects together and, at other distances, pushes them apart. The analysis underscores how hard it is to explain away dark matter.

Concocting such a theory of gravity “is so complicated that it seems very unlikely that anyone could come up with a scenario that would work,” says Scott Dodelson, a theoretical physicist at Carnegie Mellon University, who wasn’t involved in the new work. Still, some theorists say it may be possible to pass the test.

According to cosmologists’ prevailing theory, dark matter pervades pretty much every galaxy, providing the extra gravity that keeps stars from swirling out into space, given the speeds at which astronomers see the galaxies rotating. A vast web of clumps and strands of the stuff served as the scaffolding on which the cosmos developed. Yet, after of decades of trying, physicists haven’t spotted particles of dark matter floating around, and many would happily dismiss the idea—if it didn’t work so well.

Some scientists have tried to kick the dark matter habit. In 1983, Israeli physicist Mordehai Milgrom found he could account for the high speeds of stars swirling around the peripheries of galaxies by modifying Isaac Newton’s famous second law of motion: force equals mass times acceleration. That insight suggested the need for dark matter could be obviated by changing the law of gravity, at least on the scale of individual galaxies. But theorists labored for decades to turn the idea into a coherent theory of gravity akin to Albert Einstein’s general theory of relativity, and to do so, they had to add new fields, cousins of the usual gravitational field.

But to do away with dark matter, theorists would also need explain away its effects on much larger, cosmological scales. And that is much harder, argues Kris Pardo, a cosmologist at the California Institute of Technology, and David Spergel, a cosmologist at Princeton University. To make their case, they compare the distribution of ordinary matter in the early universe as revealed by measurements of the afterglow of the big bang—the cosmic microwave background (CMB)—with the distribution of the galaxies today.

The evolution of the universe is a tale of two fluids: dark matter, which doesn’t interact with light, and ordinary matter, which does. The big bang left ripples in the dark matter, which under its own gravity began to coalesce into the denser spots. Ordinary matter—then, a hot soup of free-flying protons and electrons—also began to fall into the dark matter clumps. However, those charged particles themselves generated radiation that pushed them back out, creating sound waves known as a baryon acoustic oscillations. The waves continued to spread until the universe cooled enough to form neutral atoms, 380,000 years after the big bang, when the CMB was born. The sound wave left its imprint on the CMB and, faintly, in the distribution of the galaxies.

Or could that evolution be explained with only ordinary matter interacting through modified gravity? To explore that possibility, Pardo and Spergel derived a mathematical function that describes how gravity would have had to work to get from the distribution of ordinary matter revealed by the CMB to the current distribution of the galaxies. They found something striking: That function must swing between positive and negative values, meaning gravity would be attractive at some length scales and repulsive at others, Pardo and Spergel report this week in Physical Review Letters. “And that’s superweird,” Pardo says.

The strange behavior is required to explain how the larger baryon acoustic oscillation faded over cosmic time while the smaller galaxies emerged, Pardo says. Just as Milgrom did with individual galaxies, the new work shows how, without dark matter, gravity would have to change to explain the universe’s large-scale structure, Dodelson says. But that change would have to be radical, he says. “They’re demonstrating that to do that you have to jump through these 13 hoops,” he says.

However, theorists already seem prepared to jump through those hoops. In a paper posted in June to the preprint server arXiv, theoretical cosmologists Constantinos Skordis and Tom Złosnik of the Czech Academy of Sciences present a dark matterless theory of modified gravity they say jibes with CMB data. To do that, researchers add to a theory like general relativity an additional, tunable field called a scalar field. It has energy, and through Einstein’s equivalence of mass and energy, it can behave like a form of mass. Set things up just right and at large spatial scales, the scalar field interacts only with itself and acts like dark matter.

The team hasn’t explicitly shown that the theory, which isn’t meant to be a fundamental theory of gravity, passes Pardo’s and Spergel’s particular test. But because it’s designed to mimic dark matter, it ought to, Skordis says. “We engineered it to have that behavior.”

Skordis’s and Złosnik’s paper is “very exciting,” Pardo says. But he notes that in some sense it merely replaces one mysterious thing—dark matter—with another—a carefully tuned scalar field. Given the complications, Pardo says, “dark matter is kind of the easier explanation.”

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