*Decades ago, Einstein concocted a theory in which space doesn’t just curve, but swirls like a cyclone. Now it is making a comeback because it could fix several of the biggest problems in cosmology.*

LONG ago, people thought that empty space was just what it sounds like: a featureless void. But the more we have studied seeming emptiness, the more we have shown that this is far from the truth. The air around us is full of jostling gas molecules. In space proper, beyond our atmosphere, there are quantum fields and particles of light. Even the emptiest corner of interstellar wilderness isn’t devoid of character because space itself can warp and curve.

But what if we still haven’t got to the bottom of what space is like? In the middle of his career, Albert Einstein became convinced that general relativity, his great theory of space and time, had missed a trick. Yes, space did warp and curve – but not in the way he had thought. If the true twistiness of space was accounted for, he reckoned, it might bring us closer to a grand unified theory of physics.

Einstein never quite cracked the idea, and it has been largely left to languish for almost a century. But now there is fresh cause to revive it. Physicists are struggling with a raft of devilish problems in cosmology that are forcing us to question the basics of even our most well-established theories. Dark energy, the unidentified stuff that seems to be pushing the universe apart at an ever accelerating rate, is just one example.

Some physicists are asking whether the answer to all these problems could be to once again tweak our understanding of space itself. This time the goal isn’t to unify all of physics. But if we give space the right kind of twist, it is beginning to look like many of the most vexing problems in physics could melt away.

The way we now understand space dates back to 1915, when Einstein published his theory of general relativity. It is built upwards from his realisation that the way objects respond to gravity and acceleration is indistinguishable, which we now call the equivalence principle. The theory tells us that space and time can’t be considered separately, but only as a kind of four-dimensional canvas for reality.

As if that wasn’t enough, Einstein also showed that any object with mass could warp and deform space-time, like a higher-dimensional version of a bowling ball on a trampoline. It was these undulations in space-time that gave rise to gravity. Objects falling from the sky were following invisible contour lines in the fabric of space. It is a beautiful theory that has stood the test of time. But for Einstein himself, trouble was already brewing.

In the early 1920s, he and others were laying the foundations for the most successful idea in all of physics: quantum theory. It explains the nature of the subatomic world, including electromagnetism, the force that gives rise to light and creates attractions and repulsions between charged particles. From the start, this theory forced us to leave common sense at the door. It works by predicting what will happen when an observer makes a measurement on a quantum particle, and seems to suggest that before that measurement, the particle exists in a nebulous cloud of indeterminacy. Einstein liked it not one bit; he thought the chance and imprecision at the core of the theory was a sign of our ignorance, not a true aspect of nature.

So he began work on an alternative theory of electromagnetism, one written in similar mathematical language to general relativity. To understand how it works, we need to know that mathematicians have two ways of talking about how things curve. One is simply called curvature and it describes how lines bend. Then there is a more sophisticated language called torsion, which is used to describe how things twist. You could describe a piece of wiggly spaghetti on a plate with curvature, but to define the corkscrew shape of fusilli you would need torsion.

In general relativity, Einstein had found that using a 4D version of curvature to describe space-time worked perfectly. His new plan was to develop a version of the theory using torsion instead and see if this could explain both gravity and electromagnetism in one neat package. It was a delightful idea. In the new hypothesis, massive objects and charged objects would cause space-time to twist up beneath them, like a cyclone in the fabric of reality. They would do this in slightly different ways, one giving rise to electromagnetism and the other gravity.

Einstein published this hypothesis in 1928. But he couldn’t get it to work properly – the rewritten theory was really just general relativity expressed in a new way and it couldn’t explain electromagnetism. It is known as teleparallel gravity because of the way it was initially analysed by examining parallel lines in space.

In the decades that followed, teleparallel gravity was worked on by the occasional theorist. Meanwhile, general relativity scored success after success and quantum theory matured and dominated fundamental physics. Interest in Einstein’s attempt at unification waned.

Today, physics is in a wholly different place. General relativity and quantum theory continue to be confirmed time after time. Yet it seems they can’t be the complete description of reality because they are mutually incompatible. There are also huge problems in cosmology that they can’t answer (see “Four problems, one solution“).

One of them first appeared about 20 years ago, when astronomers noticed that the rate of expansion of the universe is accelerating. We have no good explanation for this apart from to invoke an unknown substance called dark energy. The past few years have thrown up an even more embarrassing problem. We measure the rate of expansion of the universe using two different methods, one based on exploding stars and one based on the cosmic microwave background, a sea of radiation emitted shortly after the big bang. These two methods give us two quite different answers. It is still just possible that this trouble, known as the Hubble tension, could be down to a measurement error. But it is fair to say that cosmologists are in crisis mode.

One resolution might lie in accepting that general relativity doesn’t provide a perfect description of reality. In this reading, there is no dark energy – it is just that gravity itself doesn’t work quite how we thought it does.

Theorists have been producing modifications to general relativity for decades. Most focus on adding new ingredients to the formula, allowing the curvature of space-time to respond to more than the presence of matter and energy. But with so many flavours on offer, how do you discern if any are correct?

One way to judge involves gravitational waves, fluctuations in space-time that result from collisions between stars, black holes and the like. General relativity says that these waves should propagate at the speed of light. But modified theories of gravity almost always predict a slightly slower speed.

In 2017, we managed to observe the gravitational waves caused by the smashing together of two neutron stars – and the light that this produced. The flash of light and the gravitational waves arrived at Earth within seconds of each other. There was no slowing, and this result was enough to wipe almost every theory of modified gravity off the table.

### Last one standing

But not teleparallel gravity. The theory doesn’t predict any change to the speed of gravitational waves. This means that, for those who think the Hubble tension can be resolved by overhauling gravity, there are few options left except teleparallel gravity.

It is this kind of logic that motivates people like Jackson Said at the University of Malta, a leading figure in teleparallel research. “These are very exciting times, with a new synergy in the community in getting teleparallel gravity to help solve some of the big problems in modern cosmology,” says Said.

He isn’t alone in his enthusiasm. “As a cosmologist, I find teleparallel gravity very intriguing,” says Celia Escamilla-Rivera at the National Autonomous University of Mexico. “We are excited that it can shed some light on the questions that have been problems for several years in cosmology, like the nature of the dark sector.”

We have known for a long time that the equations of general relativity can be written down using the language of torsion as well as curvature, and the two work out as equivalent. This was proved back in 1976. It means that if Einstein had chosen to use torsion to write out his equations from the very start, his theory would still have worked just as well.

The audacious hope is that teleparallel gravity is actually better than general relativity. The mathematical language of torsion is more malleable than curvature, so researchers can fit terms into the equations that make matter and energy more responsive to the twistiness of space-time. In almost all circumstances, including the ordinary space in our solar system, these modifications make no noticeable difference to anything. But they would kick into gear in extreme situations, like at the big bang or on the epic scales of the entire universe – exactly where we encounter the biggest problems.

In 2018, astrophysicist Rafael Nunes at the National Institute for Space Research in Sao Paulo, Brazil, used teleparallel gravity to explore the Hubble tension. He tried a simple modification to basic teleparallel gravity and used this framework to calculate the rate of the universe’s expansion from data on the cosmic microwave background. It came out the same as the rate given by supernovae. The Hubble tension had melted away.

There are now published models of teleparallel gravity that can explain away three other big problems in cosmology too. But these each use different modifications – there is no single theory of teleparallel gravity.

Recently, however, there has been a finding that boosted the case for teleparallel gravity, one that circles back to Einstein’s original vision. One of the leading candidates for a unified theory of physics today is string theory, which says that all forces and energy in the universe arise from the vibrations of invisible strings. The theory is much maligned for its lack of testable predictions and intractable mathematics. But with a dearth of strong competitors, it still commands plenty of interest as a possible theory of everything. If it is, then a new theory of gravity should be derivable from string theory.

Earlier this year, a team of theorists led by Sebastian Bahamonde at the University of Tartu in Estonia found that teleparallel gravity is contained within string theory. They used mathematical language borrowed from string theory to derive a teleparallel-based history of the universe, and found that it mimicked many key features of our cosmological past. It is far from a closed case, but is another hint. “We do not expect that general relativity is the final theory of gravity,” says Bahamonde.

Cosmologist Eleonora Di Valentino at Durham University, UK, is paying close attention to teleparallelism. “My point of view is that at this stage all the possibilities are welcomed,” she says. “Teleparallel gravity is a quickly growing, but still very theoretical, field.”

Testing teleparallel gravity is the only way we will find out if it is correct. But that won’t be easy. The idea comes in so many flavours that no single test would prove it right or wrong. Instead, progress is more likely to come from tests that push general relativity past its breaking point. So far, Einstein’s theory has proved singularly resilient, even describing extreme scenarios like the collisions of black holes to perfection.

### Mysterious equivalence

There may be one way to directly test teleparallel gravity and that is through the equivalence principle, the bedrock idea on which general relativity is built. The principle says that an object’s gravitational mass, which responds to the warping of space-time, is the same as its inertial mass, which resists acceleration.

In general relativity, the equivalence principle has to be true, or the theory collapses. But there has never been an obvious reason this is so. All we know is that, empirically, the principle is sound – at least in all measurements we have made so far.

One manifestation of the principle is that all objects fall to Earth with the same acceleration regardless of their mass, as long as things like air resistance don’t interfere. We already know this is true to an accuracy of one part in a trillion. But if we found even the tiniest difference, that would show that general relativity is wrong and point strongly towards teleparallel gravity.

There is one proposed experiment that might just be capable of checking this. The Satellite Test of the Equivalence Principle project aims to put eight different test masses into orbit, shield them from drag and measure how they respond to Earth’s gravity in minute detail. If any difference appears between the behaviour of the masses, that would be a violation of equivalence – and teleparallelism will be right there waiting to explain the results.

Einstein himself never gave up on finding an alternative to quantum theory until his death in 1955. His forgotten theory isn’t what he once hoped it could be. But it is possible that his twisted vision of space wasn’t entirely wrong. For now, at least, Einstein’s dream is still alive.

**Four problems, one solution**

Cosmology is facing four huge, interrelated problems. A resurgent theory called teleparallel gravity might provide answers to them all

Problem 1:

**Dark matter** Beginning in the 1970s, astronomers began to realise that many galaxies are rotating so fast that they ought to spin themselves apart – unless, that is, they contain extra, invisible matter. Further evidence has led us to believe that this dark matter makes up more than 80 per cent of all matter in the universe – but we don’t know what it is.

Problem 2:

**Inflation** In order to explain how uniform the universe is on the largest scales, cosmologists think it ballooned at incredible speed soon after the big bang. But what triggered this period of inflation and what switched it off? One hypothesis involves a quantum field that has since disappeared for unexplained reasons.

Problem 3:

**Dark energy** In 1998, we discovered that the universe’s rate of expansion is accelerating. So far, all cosmologists have been able to do is give this phenomenon a name: dark energy. We have very little idea what it actually is.

Problem 4:

**The Hubble tension** We can measure the present-day expansion rate of the universe – known as the Hubble constant – in two ways, one based on nearby supernovae and another based on radiation left over from soon after the big bang, called the cosmic microwave background (CMB). The latter method gives a number that is about 10 per cent smaller than that given by the former.

Solution:

Under teleparallel gravity, there is no need to invoke dark matter or dark energy. Instead we have a different picture of how ordinary matter responds to gravity. Inflation still happens, but it is a natural consequence of the state of the early universe. The Hubble tension also disappears. If gravity operates differently to how we think on the largest scales, then we would need to tweak the way we analyse the CMB. Indeed a version of teleparallel gravity has already been shown to resolve the Hubble tension in principle (see main story).