The Universe is a strange place. Apart from the normal matter that we see around us, there appears to be a far larger amount of matter that we cannot see—the infamous dark matter. Even more puzzling, the Universe seems to be bathed in a similarly invisible dark energy, which drives the Universe to expand faster and faster. This all points to something missing from our understanding. At the moment, we tend to think that dark matter is something missing from quantum mechanics, a particle that provides dark matter. Dark energy seems to be more gravity related.

But it’s possible the two are linked. According to Professor Erik Verlinde from the University of Amsterdam, it may be that dark matter does not exist. His work indicates that in a Universe with dark energy (a positive cosmological constant), gravity does not exactly follow general relativity. His preliminary calculations indicate that the difference between general relativity and his work may provide forces that we currently ascribe to dark matter.

Getting rid of dark matter is a big, headline-grabbing claim, and Verlinde’s gotten his share of attention when he’s promoted his ideas in the past. But is there really anything to such a seemingly bold idea? We talked with the dark energy man himself to get a better idea.

## Theory vs. evidence

The evidence that we need something like dark energy and dark matter is quite strong. Based on the observed matter in a galaxy, Newton’s law of gravity (the forces are too small to require general relativity) predicts that the speed of stars should drop off further from a galaxy’s center. But the speed actually slows to some value and then stays relatively constant as you head towards the galaxy’s edges. This can be explained by some amount of additional, unobserved matter.

By itself, that would be an anomaly. But the same amount of dark matter is required to explain the Cosmic Microwave Background. The CMB has been measured with exquisite sensitivity. Cosmological models fit the measurements with mindbogglingly high precision—except for one peak in the spectrum, where dark matter has to be added to get a good fit. Since the ratio of dark matter to ordinary matter is the same for the cosmic microwave background and for galaxies (on average), this seems to strengthen the case for dark matter being a particle and not a change in the laws of gravity.

Yet we know that, at some level, our current theory of gravity must be wrong. General relativity produces infinities: at the center of a black hole, the curvature of space is infinitely tight, implying that the force of gravity is infinitely high. We don’t like that; infinities imply that things are broken.

And this is not the only place where gravity doesn’t behave quite as expected: the Universe’s rate of expansion is accelerating—again, we refer to this as dark energy. The force that drives that acceleration looks like a gravitational force and is easily incorporated into general relativity. But we don’t really know the origin of that force, and unexplained forces are not to be tolerated in physics.

If we add dark matter to the mix, we can explain the rotation curves of galaxies and the cosmic microwave background. If we add dark energy, we can explain the expansion of the Universe. It may be that the Universe is really like this, with our familiar matter accounting for only four percent of its content.

But until we have an explanation for dark matter and dark energy, it will remain unsatisfying. Which is why, even though this general understanding of the Universe works so well, some people are skeptical that the data will continue to support it. Verlinde is clearly one of them. “I want people to search for it [dark matter] as much as they can, because I’m convinced that they won’t find it,” he told Ars. “Eventually, if indeed they don’t find anything, they may start to think that, maybe, it’s something else.”

When they do, Verlinde is ready offer an alternative, having made something of a name for himself for a seemingly quite different take on gravity. But the differences in Verlinde’s views are exaggerated, according to Dr. Sabine Hossenfelder, a research fellow at the Frankfurt Institute for Advanced Studies, “It’s not so far out there,” she said. “It’s mostly his interpretation that seems to strike some people as a little odd.”

If Verlinde is right, then dark matter may actually be due to dark energy. And if Hossenfelder is right, dark energy could be a natural consequence of Verlinde’s theory. So, how does Verlinde’s approach to gravity work—and what makes other theorists think it’s so different?

## Swapping a bowl for a hill

One of the key differences between Verlinde’s approach and that of others is the space in which he works. Our Universe is expanding, and that expansion is accelerating. This is called de Sitter space, and it comes with a positive cosmological constant driving the acceleration. But it’s easier to do the mathematics in a Universe with a slowing rate of expansion and a negative cosmological constant (called anti-de Sitter space).

There are many good reasons for abandoning the Universe as we observe it for this play Universe. Among them is that the play Universe is surrounded by a horizon, and there is a relationship between the space contained within the horizon and the area of its surface. This is called the anti-de Sitter space/conformal field theory (AdS/CFT) correspondence. It basically says that the gravitational theory in the volume maps to the quantum theory on the boundary, so quantum properties, like entropy and temperature, can be obtained by solving gravitational equations in the volume. This is generally easier than the quantum theories that must be solved on the horizon.

This is a really cool trick and has inspired Verlinde to look for other horizons. Black holes showed some similarities. The entropy we measure on a black hole’s event horizon—a measure of the number of ways in which a system can be configured and still have the same energy—is determined by the gravitational equations inside the horizon. Even better, like in anti-de Sitter space, the entropy grows in proportion to the area of the horizon. While a black hole horizon does not follow the AdS/CFT correspondence as theoretical physicists know it, it’s… well, Verlinde thinks there is something to be gained from exploring the similarities.

Scientists had also found another horizon in our own Universe: the cosmological horizon. If you look out from the Earth, objects that are further away are expanding away from us faster than those that are close, as the space in between is expanding. At some distance, space ends up expanding as fast as the speed of light, so nothing reaches us from that distance or beyond. This distance is the cosmological horizon. And, according to Verlinde, the entropy on this horizon is also given by the same area law that applies to black holes and anti-de Sitter space.

In these explorations, Verlinde also rediscovered a trick. You can reverse the reasoning above. You can use the thermodynamics (entropy) of the horizon to obtain Einstein’s general relativity for the volume contained by the horizon. This is called emergent gravity.

According to Hossenfelder, emergent gravity by itself isn’t especially useful. “In the end, we already know general relativity, so you can say ‘well what’s the point?’ What is the point in showing that [general relativity] can be re-expressed as a different theory? It’s still the same outcome,” she said. “Maybe it’s a different way to calculate things. That’s nice, but not really insightful.”

While this re-casting of Einstein’s equations as a consequence of thermodynamics isn’t useful on its own, it is the foundation on which the rest of Verlinde’s work is based.