Simulating the universe using Einstein’s theory of gravity may solve cosmic puzzles

If the universe were a soup, it would be more of a chunky minestrone than a silky-smooth tomato bisque.

Sprinkled with matter that clumps together due to the insatiable pull of gravity, the universe is a network of dense galaxy clusters and filaments — the hearty beans and vegetables of the cosmic stew. Meanwhile, relatively desolate pockets of the cosmos, known as voids, make up a thin, watery broth in between.

Until recently, simulations of the cosmos’s history haven’t given the lumps their due. The physics of those lumps is described by general relativity, Albert Einstein’s theory of gravity. But that theory’s equations are devilishly complicated to solve. To simulate how the universe’s clumps grow and change, scientists have fallen back on approximations, such as the simpler but less accurate theory of gravity devised by Isaac Newton.
Relying on such approximations, some physicists suggest, could be mucking with measurements, resulting in a not-quite-right inventory of the cosmos’s contents. A rogue band of physicists suggests that a proper accounting of the universe’s clumps could explain one of the deepest mysteries in physics: Why is the universe expanding at an increasingly rapid rate?

The accepted explanation for that accelerating expansion is an invisible pressure called dark energy. In the standard theory of the universe, dark energy makes up about 70 percent of the universe’s “stuff” — its matter and energy. Yet scientists still aren’t sure what dark energy is, and finding its source is one of the most vexing problems of cosmology.

Perhaps, the dark energy doubters suggest, the speeding up of the expansion has nothing to do with dark energy. Instead, the universe’s clumpiness may be mimicking the presence of such an ethereal phenomenon.
Most physicists, however, feel that proper accounting for the clumps won’t have such a drastic impact. Robert Wald of the University of Chicago, an expert in general relativity, says that lumpiness is “never going to contribute anything that looks like dark energy.” So far, observations of the universe have been remarkably consistent with predictions based on simulations that rely on approximations.
As observations become more detailed, though, even slight inaccuracies in simulations could become troublesome. Already, astronomers are charting wide swaths of the sky in great detail, and planning more extensive surveys. To translate telescope images of starry skies into estimates of properties such as the amount of matter in the universe, scientists need accurate simulations of the cosmos’s history. If the detailed physics of clumps is important, then simulations could go slightly astray, sending estimates off-kilter. Some scientists already suggest that the lumpiness is behind a puzzling mismatch of two estimates of how fast the universe is expanding.

Researchers are attempting to clear up the debate by conquering the complexities of general relativity and simulating the cosmos in its full, lumpy glory. “That is really the new frontier,” says cosmologist Sabino Matarrese of the University of Padua in Italy, “something that until a few years ago was considered to be science fiction.” In the past, he says, scientists didn’t have the tools to complete such simulations. Now researchers are sorting out the implications of the first published results of the new simulations. So far, dark energy hasn’t been explained away, but some simulations suggest that certain especially sensitive measurements of how light is bent by matter in the universe might be off by as much as 10 percent.

Soon, simulations may finally answer the question: How much do lumps matter? The idea that cosmologists might have been missing a simple answer to a central problem of cosmology incessantly nags some skeptics. For them, results of the improved simulations can’t come soon enough. “It haunts me. I can’t let it go,” says cosmologist Rocky Kolb of the University of Chicago.

Smooth universe
By observing light from different eras in the history of the cosmos, cosmologists can compute the properties of the universe, such as its age and expansion rate. But to do this, researchers need a model, or framework, that describes the universe’s contents and how those ingredients evolve over time. Using this framework, cosmologists can perform computer simulations of the universe to make predictions that can be compared with actual observations.
After Einstein introduced his theory in 1915, physicists set about figuring out how to use it to explain the universe. It wasn’t easy, thanks to general relativity’s unwieldy, difficult-to-solve suite of equations. Meanwhile, observations made in the 1920s indicated that the universe wasn’t static as previously expected; it was expanding. Eventually, researchers converged on a solution to Einstein’s equations known as the Friedmann-Lemaître-Robertson-Walker metric. Named after its discoverers, the FLRW metric describes a simplified universe that is homogeneous and isotropic, meaning that it appears identical at every point in the universe and in every direction. In this idealized cosmos, matter would be evenly distributed, no clumps. Such a smooth universe would expand or contract over time.
A smooth-universe approximation is sensible, because when we look at the big picture, averaging over the structures of galaxy clusters and voids, the universe is remarkably uniform. It’s similar to the way that a single spoonful of minestrone soup might be mostly broth or mostly beans, but from bowl to bowl, the overall bean-to-broth ratios match.

In 1998, cosmologists revealed that not only was the universe expanding, but its expansion was also accelerating (SN: 2/2/08, p. 74). Observations of distant exploding stars, or supernovas, indicated that the space between us and them was expanding at an increasing clip. But gravity should slow the expansion of a universe evenly filled with matter. To account for the observed acceleration, scientists needed another ingredient, one that would speed up the expansion. So they added dark energy to their smooth-universe framework.

Now, many cosmologists follow a basic recipe to simulate the universe — treating the cosmos as if it has been run through an imaginary blender to smooth out its lumps, adding dark energy and calculating the expansion via general relativity. On top of the expanding slurry, scientists add clumps and track their growth using approximations, such as Newtonian gravity, which simplifies the calculations.

In most situations, Newtonian gravity and general relativity are near-twins. Throw a ball while standing on the surface of the Earth, and it doesn’t matter whether you use general relativity or Newtonian mechanics to calculate where the ball will land — you’ll get the same answer. But there are subtle differences. In Newtonian gravity, matter directly attracts other matter. In general relativity, gravity is the result of matter and energy warping spacetime, creating curves that alter the motion of objects (SN: 10/17/15, p. 16). The two theories diverge in extreme gravitational environments. In general relativity, for example, hulking black holes produce inescapable pits that reel in light and matter (SN: 5/31/14, p. 16). The question, then, is whether the difference between the two theories has any impact in lumpy-universe simulations.

Most cosmologists are comfortable with the status quo simulations because observations of the heavens seem to fit neatly together like interlocking jigsaw puzzle pieces. Predictions based on the standard framework agree remarkably well with observations of the cosmic microwave background — ancient light released when the universe was just 380,000 years old (SN: 3/21/15, p. 7). And measurements of cosmological parameters — the fraction of dark energy and matter, for example — are generally consistent, whether they are made using the light from galaxies or the cosmic microwave background.

However, the reliance on Newton’s outdated theory irks some cosmologists, creating a lingering suspicion that the approximation is causing unrecognized problems. And some cosmological question marks remain. Physicists still puzzle over what makes up dark energy, along with another unexplained cosmic constituent, dark matter, an additional kind of mass that must exist to explain observations of how galaxies and galaxy clusters rotate. “Both dark energy and dark matter are a bit of an embarrassment to cosmologists, because they have no idea what they are,” says cosmologist Nick Kaiser of École Normale Supérieure in Paris.
Dethroning dark energy
Some cosmologists hope to explain the universe’s accelerating expansion by fully accounting for the universe’s lumpiness, with no need for the mysterious dark energy.

These researchers argue that clumps of matter can alter how the universe expands, when the clumps’ influence is tallied up over wide swaths of the cosmos. That’s because, in general relativity, the expansion of each local region of space depends on how much matter is within. Voids expand faster than average; dense regions expand more slowly. Because the universe is mostly made up of voids, this effect could produce an overall expansion and potentially an acceleration. Known as backreaction, this idea has lingered in obscure corners of physics departments for decades, despite many claims that backreaction’s effect is small or nonexistent.

Backreaction continues to appeal to some researchers because they don’t have to invent new laws of physics to explain the acceleration of the universe. “If there is an alternative which is based only upon traditional physics, why throw that away completely?” Matarrese asks.

Most cosmologists, however, think explaining away dark energy just based on the universe’s lumps is unlikely. Previous calculations have indicated any effect would be too small to account for dark energy, and would produce an acceleration that changes in time in a way that disagrees with observations.

“My personal view is that it’s a much smaller effect,” says astrophysicist Hayley Macpherson of Monash University in Melbourne, Australia. “That’s just basically a gut feeling.” Theories that include dark energy explain the universe extremely well, she points out. How could that be if the whole approach is flawed?

New simulations by Macpherson and others that model how lumps evolve in general relativity may be able to gauge the importance of backreaction once and for all. “Up until now, it’s just been too hard,” says cosmologist Tom Giblin of Kenyon College in Gambier, Ohio.

To perform the simulations, researchers needed to get their hands on supercomputers capable of grinding through the equations of general relativity as the simulated universe evolves over time. Because general relativity is so complex, such simulations are much more challenging than those that use approximations, such as Newtonian gravity. But, a seemingly distinct topic helped lay some of the groundwork: gravitational waves, or ripples in the fabric of spacetime.
The Advanced Laser Interferometer Gravitational-Wave Observatory, LIGO, searches for the tremors of cosmic dustups such as colliding black holes (SN: 10/28/17, p. 8). In preparation for this search, physicists honed their general relativity skills on simulations of the spacetime storm kicked up by black holes, predicting what LIGO might see and building up the computational machinery to solve the equations of general relativity. Now, cosmologists have adapted those techniques and unleashed them on entire, lumpy universes.

The first lumpy universe simulations to use full general relativity were unveiled in the June 2016 Physical Review Letters. Giblin and colleagues reported their results simultaneously with Eloisa Bentivegna of the University of Catania in Italy and Marco Bruni of the University of Portsmouth in England.

So far, the simulations have not been able to account for the universe’s acceleration. “Nearly everybody is convinced [the effect] is too small to explain away the need for dark energy,” says cosmologist Martin Kunz of the University of Geneva. Kunz and colleagues reached the same conclusion in their lumpy-universe simulations, which have one foot in general relativity and one in Newtonian gravity. They reported their first results in Nature Physics in March 2016.

Backreaction aficionados still aren’t dissuaded. “Before saying the effect is too small to be relevant, I would, frankly, wait a little bit more,” Matarrese says. And the new simulations have potential caveats. For example, some simulated universes behave like an old arcade game — if you walk to one edge of the universe, you cross back over to the other side, like Pac-Man exiting the right side of the screen and reappearing on the left. That geometry would suppress the effects of backreaction in the simulation, says Thomas Buchert of the University of Lyon in France. “This is a good beginning,” he says, but there is more work to do on the simulations. “We are in infancy.”

Different assumptions in a simulation can lead to disparate results, Bentivegna says. As a result, she doesn’t think that her lumpy, general-relativistic simulations have fully closed the door on efforts to dethrone dark energy. For example, tricks of light might be making it seem like the universe’s expansion is accelerating, when in fact it isn’t.

When astronomers observe far-away sources like supernovas, the light has to travel past all of the lumps of matter between the source and Earth. That journey could make it look like there’s an acceleration when none exists. “It’s an optical illusion,” Bentivegna says. She and colleagues see such an effect in a simulation reported in March in the Journal of Cosmology and Astroparticle Physics. But, she notes, this work simulated an unusual universe, in which matter sits on a grid — not a particularly realistic scenario.

For most other simulations, the effect of optical illusions remains small. That leaves many cosmologists, including Giblin, even more skeptical of the possibility of explaining away dark energy: “I feel a little like a downer,” he admits.
Surveying the skies
Subtle effects of lumps could still be important. In Hans Christian Andersen’s “The Princess and the Pea,” the princess felt a tiny pea beneath an impossibly tall stack of mattresses. Likewise, cosmologists’ surveys are now so sensitive that even if the universe’s lumps have a small impact, estimates could be thrown out of whack.

The Dark Energy Survey, for example, has charted 26 million galaxies using the Victor M. Blanco Telescope in Chile, measuring how the light from those galaxies is distorted by the intervening matter on the journey to Earth. In a set of papers posted online August 4 at arXiv.org, scientists with the Dark Energy Survey reported new measurements of the universe’s properties, including the amount of matter (both dark and normal) and how clumpy that matter is (SN: 9/2/17, p. 32). The results are consistent with those from the cosmic microwave background — light emitted billions of years earlier.

To make the comparison, cosmologists took the measurements from the cosmic microwave background, early in the universe, and used simulations to extrapolate to what galaxies should look like later in the universe’s history. It’s like taking a baby’s photograph, precisely computing the number and size of wrinkles that should emerge as the child ages and finding that your picture agrees with a snapshot taken decades later. The matching results so far confirm cosmologists’ standard picture of the universe — dark energy and all.

“So far, it has not yet been important for the measurements that we’ve made to actually include general relativity in those simulations,” says Risa Wechsler, a cosmologist at Stanford University and a founding member of the Dark Energy Survey. But, she says, for future measurements, “these effects could become more important.” Cosmologists are edging closer to Princess and the Pea territory.

Those future surveys include the Dark Energy Spectroscopic Instrument, DESI, set to kick off in 2019 at Kitt Peak National Observatory near Tucson; the European Space Agency’s Euclid satellite, launching in 2021; and the Large Synoptic Survey Telescope in Chile, which is set to begin collecting data in 2023.

If cosmologists keep relying on simulations that don’t use general relativity to account for lumps, certain kinds of measurements of weak lensing — the bending of light due to matter acting like a lens — could be off by up to 10 percent, Giblin and colleagues reported at arXiv.org in July. “There is something that we’ve been ignoring by making approximations,” he says.

That 10 percent could screw up all kinds of estimates, from how dark energy changes over the universe’s history to how fast the universe is currently expanding, to the calculations of the masses of ethereal particles known as neutrinos. “You have to be extremely certain that you don’t get some subtle effect that gets you the wrong answers,” Geneva’s Kunz says, “otherwise the particle physicists are going to be very angry with the cosmologists.”

Some estimates may already be showing problem signs, such as the conflicting estimates of the cosmic expansion rate (SN: 8/6/16, p. 10). Using the cosmic microwave background, cosmologists find a slower expansion rate than they do from measurements of supernovas. If this discrepancy is real, it could indicate that dark energy changes over time. But before jumping to that conclusion, there are other possible causes to rule out, including the universe’s lumps.

Until the issue of lumps is smoothed out, scientists won’t know how much lumpiness matters to the cosmos at large. “I think it’s rather likely that it will turn out to be an important effect,” Kolb says. Whether it explains away dark energy is less certain. “I want to know the answer so I can get on with my life.”