Searching through existing data spanning 9 billion years, a University of Michigan physicist and colleagues have uncovered the first evidence of “cosmological coupling”—a newly predicted phenomenon in Einstein’s theory of gravity, possible only when black holes are placed inside an evolving universe.

Gregory Tarlé, U-M professor of physics, and researchers from the University of Hawaii and other institutions across nine countries studied supermassive black holes at the heart of ancient and dormant galaxies to develop a description of them that agrees with observations from the past decade. Their findings are published in two journal articles, one in The Astrophysical Journal and the other in The Astrophysical Journal Letters.

The first study found that these black holes gain mass over billions of years in a way that can’t easily be explained by standard galaxy and black hole processes, such as mergers or accretion of gas. According to the second paper, the growth in mass of these black holes matches predictions for black holes that not only cosmologically couple, but also enclose vacuum energy—material that results from squeezing matter as much as possible without breaking Einstein’s equations, thus avoiding a singularity.

With singularities removed, the paper then shows that the combined vacuum energy of black holes produced in the deaths of the universe’s first stars agrees with the measured quantity of dark energy in our universe.

“We’re really saying two things at once: that there’s evidence the typical black hole solutions don’t work for you on a long, long timescale, and we have the first proposed astrophysical source for dark energy,” said Duncan Farrah, University of Hawaii astronomer and lead author on both papers.

“What that means, though, is not that other people haven’t proposed sources for dark energy, but this is the first observational paper where we’re not adding anything new to the universe as a source for dark energy: Black holes in Einstein’s theory of gravity are the dark energy.”

These new measurements, if supported by further evidence, redefine our understanding of what a black hole is.

Nine billion years ago

In the first study, the team determined how to use existing measurements of black holes to search for cosmological coupling.

“My interest in this project was really born from a general interest in trying to determine observational evidence that supports a model for black holes that works regardless of how long you look at them,” Farrah said. “That’s a very, very difficult thing to do in general, because black holes are incredibly small, they’re incredibly difficult to observe directly, and they are a long, long way away.”

Black holes are also hard to observe over long timescales. Observations can be made over a few seconds, or tens of years at most—not enough time to detect how a black hole might change over the lifetime of the universe. To see how black holes change over a scale of billions of years is a bigger task.

“You would have to identify a population of black holes and determine their distribution of mass billions of years ago. Then you would have to see the same population, or an ancestrally connected population, at present day and again be able to measure their mass,” Tarlé said. “That’s a really difficult thing to do.”

Because galaxies can have life spans of billions of years, and most galaxies contain a supermassive black hole, the team realized that galaxies held the key, but choosing the right types of galaxies was essential.

“There were many different behaviors for black holes in galaxies measured in the literature, and there wasn’t really any consensus,” said study co-author Sara Petty, a galaxy expert at NorthWest Research Associates. “We decided that by focusing only on black holes in passively evolving elliptical galaxies, we could help to sort this thing out.”

Elliptical galaxies are enormous and formed early. They are like fossils of galaxy assembly. Astronomers believe them to be the final result of galaxy collisions, behemoths with upwards of trillions of old stars.

“These galaxies are ancient, don’t form many new stars, and there is very little gas left between those stars. No food for black holes,” Tarlé said.

By looking at only elliptical galaxies with no recent activity, the team could argue that any changes in the galaxies’ black hole masses couldn’t easily be caused by other known processes. Using these populations, the team then examined how the mass of their central black holes changed over the past 9 billion years.

If mass growth of black holes only occurred through accretion or merger, then the masses of these black holes would not be expected to change much at all. But if black holes gain mass by coupling to the expanding universe, then these passively evolving elliptical galaxies might reveal this phenomenon.

The researchers found that the further back in time they looked, the smaller the black holes were in mass, relative to their masses today. These changes were big: The black holes were anywhere from 7 to 20 times larger today than they were 9 billion years ago—big enough that the researchers suspected cosmological coupling could be the culprit.

Unlocking black holes

In the second study, the team investigated whether the growth in black holes measured in the first study could be explained by cosmological coupling alone.

“Here’s a toy analogy. You can think of a coupled black hole like a rubber band, being stretched along with the universe as it expands,” said study co-author and University of Hawaii theoretical astrophysicist Kevin Croker. “As it stretches, its energy increases. Einstein’s E = mc2 tells you that mass and energy are proportional, so the black hole mass increases, too.”

How much the mass increases depends on the coupling strength, a variable the researchers call k.

“The stiffer the rubber band, the harder it is to stretch, so the more energy when stretched. In a nutshell, that’s k,” Croker said.

Because mass growth of black holes from cosmological coupling depends on the size of the universe, and the universe was smaller in the past, the black holes in the first study must be less massive by the correct amount in order for the cosmological coupling explanation to work.

The team examined five different black hole populations in three different collections of elliptical galaxies, taken from when the universe was roughly one half and one third of its present size. In each comparison, they measured that k was nearly positive 3.

This value was predicted for black holes that contain vacuum energy, instead of a singularity, four years earlier by Croker, then a graduate student, and University of Hawaii professor of mathematics Joel Weiner.

The conclusion is profound: Croker and Weiner had already shown that if k is 3, then all black holes in the universe collectively contribute a nearly constant dark energy density, just like measurements of dark energy suggest.

“Is it enough?” Tarlé said. “Are the black holes made over time enough to account for 70% of the energy in the universe today?”

Black holes come from dead large stars, so if you know how many large stars you are making, you can estimate how many black holes you are making and how much they grow as a result of cosmological coupling. Using the very latest measurements of the rate of earliest star formation provided by the James Webb Space Telescope, the team found that the numbers line up.

The researchers say their studies provide a framework for theoretical physicists and astronomers to further test—and for the current generation of dark energy experiments such as the Dark Energy Spectroscopic Instrument and the Dark Energy Survey—to shed light on the idea.

“If cosmological coupling is confirmed, it would mean that black holes never entirely disconnect from our universe, that they continue to exert a major influence on the evolution of the universe into the distant future” Tarlé said.

“The question of the nature of dark energy is perhaps the most important unanswered question in contemporary physics. It’s the majority, 70% of the energy of the universe. And now we finally have observational evidence of where it comes from, why 70% and why it’s here now. It’s very exciting!”