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.

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.)