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NOT so long ago, in a galaxy really rather close by, a small band of rebels has taken up arms to overthrow a dark empire…

No, this isn’t bad Star Wars fan fiction. It’s a pretty good description of a battle for cosmology going on right now. On one side is the mighty firepower of cosmology’s standard model. It brings order to everything from the patterns in the big bang’s afterglow to the evolution of galaxies. But it can only do so using dark powers. There’s dark matter, an additional unseen stuff amounting to a quarter of everything in the universe, which keeps galaxies and clusters of galaxies in line and stops them from flying apart. Far outgunning even this, however, is dark energy. Representing more than two-thirds of the universe, dark energy is a mysterious, expansionist force whose very identity is unknown – but which has dominated the cosmos for the past 5 billion years.

Not for much longer, if the rebels lining up on the other side against the universe’s established order have anything to do with it. “In 10 years’ time, dark energy is gone,” says of Claude Bernard University in Lyon, France. Dark energy’s power, the insurgents claim, is a mere illusion created by the machinery of the standard model itself. They now aim to bring it down.

At the heart of this unbalanced conflict lies a founding principle of the universe – or at least, of cosmology since the days of Copernicus. He argued in the 16th century that Earth didn’t occupy any special place in the universe. This assertion has since morphed into the “cosmological principle”, which states that the universe is more or less the same no matter where you are or whichever direction you look. These twin assumptions of homogeneity and isotropy amount to saying the universe has no special places whatsoever.

They proved a boon when trying to extract workable models of the universe from the equations of general relativity. General relativity is Einstein’s theory of how matter, space and time interact to produce the force we know as gravity. Its guiding principle was once succinctly summed up by physicist John Wheeler as “Matter tells space how to curve; space tells matter how to move”.

The devil is in the detail. General relativity’s equations are notoriously intractable. On one side of them are mathematical terms for things that warp space and time – matter, energy. On the other side are descriptions of their effects: how fast space-time is expanding and its curvature.

With curvature, there are three main options. Space-time can be folded in on itself as if it were on the surface of a four-dimensional sphere, producing a “closed” universe with positive curvature. Or it can be folded outwards to produce an “open” geometry said to have negative curvature. Lastly, it can be broadly “flat” with zero curvature, like the surface of a sheet of paper, only in four dimensions.

Building a cosmological model means balancing all these terms for the entire universe: the right amount of stuff to produce the right expansion and curvature. Assuming a uniform universe where matter and energy are evenly spread and an overall average curvature that doesn’t change in time or space makes that job more manageable. “It’s an assumption that is made for reasons of mathematical simplicity,” says of the University of Canterbury in Christchurch, New Zealand.

It’s still a hard task. When Einstein first attempted it, the universe was thought to be static, neither expanding nor contracting, but the solutions he came up with predicted a dynamic universe that was either expanding or contracting, and definitely not static. His sticking-plaster fix was to introduce a new term, a “cosmological constant“, to provide some extra energy that stabilised the universe.

Soon after, Edwin Hubble and others showed that the universe was indeed expanding. Einstein graciously took out the cosmological constant, calling it his greatest blunder. Others then found the solutions to his equations that corresponded to just the sort of expanding cosmos that the universe seemed to be. This “Friedmann–Lemaître–Robertson–Walker” (FLRW) solution, which assumes the universe to be flat, homogeneous and isotropic, became the bedrock of the standard model of the big bang universe.

Over the years, this model has been refined with observational evidence. Studies of the cosmic microwave background – light emitted when the cosmos was about 400,000 years old – confirm the idea of a smooth, largely homogeneous universe, and also indicate that the universe back then was almost completely flat, with zero curvature.

The standard model has also proved itself adept at adapting to changing realities. The discovery that galaxies and clusters of galaxies were rotating too fast for the amount of visible matter they contained was solved by adding dark matter to the mix – more matter for the matter side of the equations.

“Dark energy is an illusion created by the machinery of our cosmological model”

The shock discovery by two teams independently in 1998 that distant supernovae were fainter than expected was more problematic. These supernovae seemed to be farther away than they would have been if the universe had been expanding at the same rate since the big bang. Sometime around 5 billion years ago, the universe’s expansion had begun to accelerate – an odd development, given that the gravitational pull of all the matter in the universe should, if anything, have put a brake on the expansion.

Wobbly orthodoxy

This is where dark energy entered the picture. It was effectively a new lease of life for Einstein’s cosmological constant. Add this extra term back into the FLRW model on the matter and energy side and you can make the equations balance out, while reproducing an accelerating expansion of a flat universe.

The vast majority of cosmologists are perfectly happy with this solution: it works, sort of. But while recent measurements suggest the amount of extra expansion is bigger than even dark energy can explain on its own (91av, 11 June, p 8), there is a bigger problem. The latest calculations suggest dark energy makes up 68.3 per cent of all the stuff there is – yet no one has the slightest clue what it is.

This wobbly orthodoxy is what the rebels are seeking to undermine. Abandon the assumption that the universe is uniform and unchangingly flat, they say, and you can eliminate dark energy, too.

As heretical as Copernicus back in the day? Perhaps, but perhaps not. The universe might once have looked broadly homogeneous, but it is hard to claim that today. Already in the cosmic microwave background you see the seeds of the galaxies and clusters of galaxies that gravity’s pull has constructed over time. As the universe has evolved, a web of over-dense regions has gradually formed, with huge under-dense voids opening up between them. The question is, what effect has this changing distribution of matter had on the space-time around it? “Are the effects of structures really negligible?” says of the University of Helsinki, Finland. “That has not been satisfactorily answered.”

The simple answer is there must be some sort of effect. Matter tells space how to curve, so the extra mass of galaxies and galaxy clusters will increase the curvature of nearby space-time, making it more positive. Meanwhile voids will cause their local space-time to warp the other way, giving it a negative curvature. That much is bog-standard general relativity.

The controversial question is whether these “backreaction” effects between matter and space-time add up to enough to change the geometry of the universe as a whole. For matter and energy, a strict law of conservation means their total amount cannot change over time. But no such restriction exists for curvature.

In the alternative backreaction picture, as matter clumps into ever denser, more compact structures, the proportion of the universe that is void increases, pushing its overall average curvature into negative territory. In a model with backreaction and a universe whose curvature goes negative over time, light’s path will become distorted that things look more distant than in a flat space-time (see diagram). Thus you can build models in which there is no accelerated expansion, and hence no dark energy.

This does away with another problem, too. In the standard model, it’s difficult to explain why dark energy’s effects kick in only about 5 billion years ago, some 9 billion years into the universe’s history. That’s a crucial point: had dark energy dominated earlier, the universe would have blown apart so quickly we would have had no galaxies, no life and no physicists wondering about appropriate models of the universe. With backreaction, there’s nothing to explain: 5 billion years ago is the point in the progressive evolution of structures when voids begin to dominate and the overall curvature goes negative.

So there’s a case to answer, says Räsänen. “It’s not been established beyond reasonable doubt that dark energy exists,” he says. “But I’d never say that it has been established that dark energy does not exist,” he adds. Wiltshire, like Buchert, is more forthright, styling himself an out-and-out “backreactionista”. “There is no dark energy, as far as I’m concerned,” he says. Buchert even thinks that backreaction might get rid of that other dark spectre, dark matter (see “Matter of fiction“).

Bold statements – but where’s the proof? The backreactionistas say they can fit existing observations to models that don’t include dark energy. The key is to figure out how the changes in the local curvature of space-time alter the overall, average curvature. But that’s easier said than done. The mathematics is as intractable as ever, and there is no single accepted way of calculating the average curvature of space-time in a lumpy universe.

“The universe might once have looked uniform, but it is hard to claim that today”

All this leaves some unimpressed. of Johns Hopkins University in Baltimore, Maryland, was a leader of one of the teams that made the 1998 supernova measurements, and won a share of the 2011 Nobel prize in physics for his efforts. “In the mainstream cosmology community this is not even discussed,” he says. Local changes in curvature are unlikely to change the overall average curvature of the universe, he says. “It is as if someone wondered what the impact of many rounding errors was on the national debt and then claimed it was enough to cover the whole debt.”

Stephen Green of the Perimeter Institute in Waterloo, Canada, and Robert Wald of the University of Chicago have put the mathematical boot in. In 2014, they claimed proof that backreaction would not have any significant effect (). Last year Buchert, Räsänen, Wiltshire and others hit back, arguing that Green and Wald’s assumptions fail to include the essential physics of backreaction. In a paper titled “Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?” they open with the blunt statement “No.” ().

The best way to mediate the conflict would be to build general relativistic models that simulate the evolution of a realistic universe containing the sort of structures that our cosmos does. Until recently, the huge computational demands of such an endeavour made it impossible. But now of Case Western Reserve University in Cleveland, Ohio, and his colleagues have been having a go, as has another team.

“It’s as if someone claimed rounding errors explained the entire national debt”

The preliminary results have just passed peer review and are set for publication. They suggest that backreaction effects do exist – but they aren’t enough to provide the sort of effects needed to square with observations ().

Buchert and Wiltshire point out that these models don’t yet allow the average curvature of space-time to evolve over time. And Starkman himself cautions that the models are still crude: the distribution of matter is still not fine-grained enough to be entirely realistic, and matter is modelled as a fluid, not particles. Still, he thinks that the backreaction is unlikely to have the large effect that the renegades expect. “It’s not how I’d bet, from my understanding of our preliminary results,” he says. “It’s not how I’d have bet before, but I respect the people in the backreaction group far too much to be willing to say that they are wrong without checking.”

So could this revolution be a damp squib – leaving the dark shadows to continue to haunt the cosmos? The backreactionistas aren’t giving up the fight in a hurry. They are working on models that can be tested against more observations, while Wiltshire and Buchert are also studying backreaction in the primordial universe. For Wiltshire, in the end it’s not about necessarily being correct, but about asking the right questions – and as long as dark energy can’t be explained, those questions are there to be asked. “As far as I’m concerned, whether I’m right or wrong, I’m doing the right thing,” he says.

This article appeared in print under the headline “Out of the shadows”