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Troubled Times for Alternatives to Einstein’s Theory of Gravity

Miguel Zumalacárregui knows what it feels like when theories die. In September 2017, he was at the Institute for Theoretical Physics in Saclay, near Paris, to speak at a meeting about dark energy and modified gravity. The official news had not yet broken about an epochal astronomical measurement—the detection, by gravitational wave detectors as well as many other telescopes, of a collision between two neutron stars—but a controversial tweet had lit a firestorm of rumor in the astronomical community, and excited researchers were discussing the discovery in hushed tones.

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Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

Zumalacárregui, a theoretical physicist at the Berkeley Center for Cosmological Physics, had been studying how the discovery of a neutron-star collision would affect so-called “alternative” theories of gravity. These theories attempt to overcome what many researchers consider to be two enormous problems with our understanding of the universe. Observations going back decades have shown that the universe appears to be filled with unseen particles—dark matter—as well as an anti-gravitational force called dark energy. Alternative theories of gravity attempt to eliminate the need for these phantasms by modifying the force of gravity in such a way that it properly describes all known observations—no dark stuff required.

At the meeting, Zumalacárregui joked to his audience about the perils of combining science and Twitter, and then explained what the consequences would be if the rumors were true. Many researchers knew that the merger would be a big deal, but a lot of them simply “hadn’t understood their theories were on the brink of demise,” he later wrote in an email. In Saclay, he read them the last rites. “That conference was like a funeral where we were breaking the news to some attendees.”

The neutron-star collision was just the beginning. New data in the months since that discovery have made life increasingly difficult for the proponents of many of the modified-gravity theories that remain. Astronomers have analyzed extreme astronomical systems that contain spinning neutron stars, or pulsars, to look for discrepancies between their motion and the predictions of general relativity—discrepancies that some theories of alternative gravity anticipate. These pulsar systems let astronomers probe gravity on a new scale and with new precision. And with each new observation, these alternative theories of gravity are having an increasingly hard time solving the problems they were invented for. Researchers “have to sweat some more trying to get new physics,” said Anne Archibald, an astrophysicist at the University of Amsterdam.

Searching for Vulcan

Confounding observations have a way of leading astronomers to desperate explanations. On the afternoon of March 26, 1859, Edmond Lescarbault, a young doctor and amateur astronomer in Orgères-en-Beauce, a small village south of Paris, had a break between patients. He rushed to a tiny homemade observatory on the roof of his stone barn. With the help of his telescope, he spotted an unknown round object moving across the face of the sun.

He quickly sent news of this discovery to Urbain Le Verrier, the world’s leading astronomer at the time. Le Verrier had been trying to account for an oddity in the movement of the planet Mercury. All other planets orbit the sun in perfect accord with Isaac Newton’s laws of motion and gravitation, but Mercury appeared to advance a tiny amount with each orbit, a phenomenon known as perihelion precession. Le Verrier was certain that there had to be an invisible “dark” planet tugging on Mercury. Lescarbault’s observation of a dark spot transiting the sun appeared to show that the planet, which Le Verrier named Vulcan, was real.

It was not. Lescarbault’s sightings were never confirmed, and the perihelion precession of Mercury remained a puzzle for nearly six more decades. Then Einstein developed his theory of general relativity, which straightforwardly predicted that Mercury should behave the way it does.

A map of the solar system from 1846 shows the presumed orbit of Vulcan, a hypothetical planet that was invoked to explain a puzzling feature of Mercury’s orbit.

In Le Verrier’s impulse to explain puzzling observations by introducing a heretofore hidden object, some modern-day researchers see parallels to the story of dark matter and dark energy. For decades, astronomers have noticed that the behavior of galaxies and galaxy clusters doesn’t seem to fit the predictions of general relativity. Dark matter is one way to explain that behavior. Likewise, the accelerating expansion of the universe can be thought of as being powered by a dark energy.

All attempts to directly detect dark matter and dark energy have failed, however. That fact “kind of leaves a bad taste in some people’s mouths, almost like the fictional planet Vulcan,” said Leo Stein, a theoretical physicist at the California Institute of Technology. “Maybe we’re going about it all wrong?”

For any alternative theory of gravity to work, it has to not only do away with dark matter and dark energy, but also reproduce the predictions of general relativity in all the standard contexts. “The business of alternative gravity theories is a messy one,” Archibald said. Some would-be replacements for general relativity, like string theory and loop quantum gravity, don’t offer testable predictions. Others “make predictions that are spectacularly wrong, so the theorists have to devise some kind of a screening mechanism to hide the wrong prediction on scales we can actually test,” she said.

The best-known alternative gravity theories are known as modified Newtonian dynamics, commonly abbreviated to MOND. MOND-type theories attempt to do away with dark matter by tweaking our definition of gravity. Astronomers have long observed that the gravitational force due to ordinary matter doesn’t appear to be sufficient to keep rapidly moving stars inside their galaxies. The gravitational pull of dark matter is assumed to make up the difference. But according to MOND, there are simply two kinds of gravity. In regions where the force of gravity is strong, bodies obey Newton’s law of gravity, which states that the gravitational force between two objects decreases in proportion to the square of the distance that separates them. But in environments of extremely weak gravity—like the outer parts of a galaxy—MOND suggests that another type of gravity is in play. This gravity decreases more slowly with distance, which means that it doesn’t weaken as much. “The idea is to make gravity stronger when it should be weaker, like at the outskirts of a galaxy,” Zumalacárregui said.

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Then there is TeVeS (tensor-vector-scalar), MOND’s relativistic cousin. While MOND is a modification of Newtonian gravity, TeVeS is an attempt to take the general idea of MOND and make it into a full mathematical theory that can be applied to the universe as a whole—not just to relatively small objects like solar systems and galaxies. It also explains the rotation curves of galaxies by making gravity stronger on their outskirts. But TeVeS does so by augmenting gravity with “scalar” and “vector” fields that “essentially amplify gravity,” said Fabian Schmidt, a cosmologist at the Max Planck Institute for Astrophysics in Garching, Germany. A scalar field is like the temperature throughout the atmosphere: At every point it has a numerical value but no direction. A vector field, by contrast, is like the wind: It has both a value (the wind speed) and a direction.

There are also so-called Galileon theories—part of a class of theories called Horndeski and beyond-Horndeski—which attempt to get rid of dark energy. These modifications of general relativity also introduce a scalar field. There are many of these theories (Brans-Dicke theory, dilaton theories, chameleon theories and quintessence are just some of them), and their predictions vary wildly among models. But they all change the expansion of the universe and tweak the force of gravity. Horndeski theory was first put forward by Gregory Horndeski in 1974, but the wider physics community took note of it only around 2010. By then, Zumalacárregui said, “Gregory Horndeski [had] quit science and [become] a painter in New Mexico.”

There are also stand-alone theories, like that of physicist Erik Verlinde. According to his theory, the laws of gravity arise naturally from the laws of thermodynamics just like “the way waves emerge from the molecules of water in the ocean,” Zumalacárregui said. Verlinde wrote in an email that his ideas are not an “alternative theory” of gravity, but “the next theory of gravity that contains and transcends Einstein’s general relativity.” But he is still developing his ideas. “My impression is that the theory is still not sufficiently worked out to permit the kind of precision tests we carry out,” Archibald said. It’s built on “fancy words,” Zumalacárregui said, “but no mathematical framework to compute predictions and do solid tests.”

The predictions made by other theories differ in some way from those of general relativity. Yet these differences can be subtle, which makes them incredibly difficult to find.

Consider the neutron-star merger. At the same time that the Laser Interferometer Gravitational-Wave Observatory (LIGO) spotted the gravitational waves emanating from the event, the space-based Fermi satellite spotted a gamma ray burst from the same location. The two signals had traveled across the universe for 130 million years before arriving at Earth just 1.7 seconds apart.

These nearly simultaneous observations “brutally and pitilessly murdered” TeVeS theories, said Paulo Freire, an astrophysicist at the Max Planck Institute for Radio Astronomy in Bonn, Germany. “Gravity and gravitational waves propagate at the speed of light, with extremely high precision—which is not at all what was predicted by those [alternative] theories.”

The same fate overtook some Galileon theories that add an extra scalar field to explain the universe’s accelerated expansion. These also predict that gravitational waves propagate more slowly than light. The neutron-star merger killed those off too, Schmidt said.

Further limits come from new pulsar systems. In 2013, Archibald and her colleagues found an unusual triple system: a pulsar and a white dwarf that orbit one another, with a second white dwarf orbiting the pair. These three objects exist in a space smaller than Earth’s orbit around the sun. The tight setting, Archibald said, offers ideal conditions for testing a crucial aspect of general relativity called the strong equivalence principle, which states that very dense strong-gravity objects such as neutron stars or black holes “fall” in the same way when placed in a gravitational field. (On Earth, the more familiar weak equivalence principle states that, if we ignore air resistance, a feather and a brick will fall at the same rate.)

The triple system makes it possible to check whether the pulsar and the inner white dwarf fall exactly the same way in the gravity of the outer white dwarf. Alternative-gravity theories assume that the scalar field generated in the pulsar should bend space-time in a much more extreme way than the white dwarf does. The two wouldn’t fall in a similar manner, leading to a violation of the strong equivalence principle and, with it, general relativity.

Over the past five years, Archibald and her team have recorded 27,000 measurements of the pulsar’s position as it orbits the other two stars. While the project is still a work in progress, it looks as though the results will be in total agreement with Einstein, Archibald said. “We can say that the degree to which the pulsar behaves abnormally is at most a few parts in a million. For an object with such strong gravity to still follow Einstein’s predictions so well, if there is one of these scalar fields, it has to have a really tiny effect.”

The test, which should be published soon, will put the best constraints yet on a whole group of alternative gravity theories, she added. If a theory only works with some additional scalar field, then the field should change the behavior of the pulsar. “We have such sensitive tests of general relativity that they need to somehow hide the theory’s new behavior in the solar system and in pulsar systems like ours,” Archibald said.

The data from another pulsar system dubbed the double pulsar, meanwhile, was originally supposed to eliminate the TeVeS theories. Detected in 2003, the double pulsar was until recently the only binary neutron-star system where both neutron stars were pulsars. Freire and his colleagues have already confirmed that the double pulsar’s behavior is perfectly in line with general relativity. Right before LIGO’s October announcement of a neutron-star merger, the researchers were going to publish a paper that would kill off TeVeS. But LIGO did the job for them, Freire said. “We need not go through that anymore.”

Slippery Survivors

A few theories have survived the LIGO blow—and will probably survive the upcoming pulsar data, Zumalacárregui said. There are some Horndeski and beyond-Horndeski theories that do not change the speed of gravitational waves. Then there are so-called massive gravity theories. Ordinarily, physicists assume that the particle associated with the force of gravity—the graviton—has no mass. In these theories, the graviton has a very small but nonzero mass. The neutron-star merger puts tough limits on these theories, Zumalacárregui said, since a massive graviton would travel more slowly than light. But in some theories the mass is assumed to be extremely small, at least 20 orders of magnitude lower than the neutrino’s, which means that the graviton would still move at nearly the speed of light.

There are a few other less well-known survivors, some of which are important to keep exploring, Archibald said, as long as dark matter and dark energy remain elusive. “Dark energy might be our only observational clue pointing to a new and better theory of gravity—or it might be a mysterious fluid with strange properties, and nothing to do with gravity at all,” she said.

Still, killing off theories is simply how science is supposed to work, argue researchers who have been exploring alternative gravity theories. “This is what we do all the time, put forward a working hypothesis and test it,” said Enrico Barausse of the Astrophysics Institute of Paris, who has worked on MOND-like theories. “99.9 percent of the time you rule out the hypothesis; the remaining 0.1 percent of the time you win the Nobel Prize.”

Zumalacárregui, who has also worked on these theories, was “sad at first” when he realized that the neutron star merger detection had proven Galileon theories wrong, but ultimately “very relieved it happened sooner rather than later,” he said. LIGO had been just about to close down for 18 months to upgrade the detector. “If the event had been a bit later, I would still be working on a wrong theory.”

Anne Archibald, an astronomer at the University of Amsterdam, has been studying the triple system to understand the behavior of gravity.

Cees Bassa

So what’s next for general relativity and modified-gravity theories? “That question keeps me up at night more than I’d like,” Zumalacárregui said. “The good news is that we have narrowed our scope by a lot, and we can try to understand the few survivors much better.”

Schmidt thinks it’s necessary to measure the laws of gravity on large scales as directly as possible, using ongoing and future large galaxy surveys. “For example, we can compare the effect of gravity on light bending as well as galaxy velocities, typically predicted to be different in modified-gravity theories,” he said. Researchers also hope that future telescopes such as the Square Kilometer Array will discover more pulsar systems and provide better accuracy in pulsar timing to further improve gravity tests. And a space-based replacement for LIGO called LISA will study gravitational waves with exquisite accuracy—if indeed it launches as planned in the mid-2030s. “If that does not see any deviations from general relativity, I don’t know what will,” said Barausse.

But many physicists agree that it will take a long time to get rid of most alternative gravity models. Theorists have dozens of alternative gravity theories that could potentially explain dark matter and dark energy, Freire said. Some of these theories can’t make testable predictions, Archibald said, and many “have a parameter, a ‘knob’ you can turn to make them pass any test you like,” she said. But at some point, said Nicolas Yunes, a physicist at Montana State University, “this gets silly and Occam’s razor wins.”

Still, “fundamentally we know that general relativity is wrong,” Stein said. “At the very core there must be some breakdown” at the quantum level. “Maybe we won’t see it from astronomical observations … but we owe it to ourselves, as empirical scientists, to check whether or not our mathematical models are working at these scales.”

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.


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