TRILLIONS of years from now, long after the sun grows to engulf Earth and then shrinks into a dim remnant of its former self, the universe will enter a quiet retirement. Thanks to its continued expansion, clusters of once-neighbouring galaxies will begin zooming away from each other so fast that even light won’t be able to bridge the gap. Stars will burn out and die. Darkness will fall across the cosmos.
At least, that is the most popular scenario. The cold, lonely immortality of this “big freeze” is a direct consequence of the standard model of cosmology, our best description of the universe. It depends on all manner of assumptions, not least that dark energy, the mysterious force thought to be causing the expansion of the cosmos to accelerate, will always have the same unvarying strength.
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But some cosmologists think that instead of dark energy remaining forever constant, it might diminish over time, causing the universe to collapse in on itself in a big crunch, a reverse of the big bang. Others think dark energy could be growing in potency, heralding a future where the universe could expand so far so fast that the fabric of space-time starts to tear itself apart. This outcome is called the big rip.
Freeze, crunch or rip? Or none of the above? That fourth possibility is the startling conclusion of the latest attempt to divine the fate of the universe. By invoking other mysterious spectres that haunt the cosmos besides dark energy, it suggests a far weirder turn of events: that the universe may be destined not exactly to end, but to evolve into a state we don’t even currently have the language to describe.
Dark energy is the most important discovery in modern cosmology. In the late 1990s, astronomers found that the expansion of our universe, rather than slowing down with age, is accelerating. Their first instinct was to attribute this to the energy of the vacuum of space-time itself, potentially the result of particles spontaneously appearing and disappearing in otherwise empty space.
But when this vacuum energy is calculated using the principles of quantum physics, it turns out to be impossibly large. “The vacuum energy would have accelerated the universe to such large scales that the first stars and galaxies wouldn’t have formed,” says Catherine Heymans, an observational cosmologist at the University of Edinburgh, UK. To avoid this problem, physicists thought that they could dream up quantum processes to cancel each other out, leading to a vacuum energy of zero. In theoretical physics, says Heymans, “it’s relatively easy to set something to zero”.
But dark energy, and by extension vacuum energy, turned out not to be zero. Most observations suggest that the vacuum energy for some given volume of space-time in our universe – the dark energy density – is constant over time. This is often called the cosmological constant, and is taken to represent the strength of dark energy. However, explaining its near zero but positive value proved extremely difficult.
These turbulent waters were ideal territory for another attempt to describe the underlying nature of the universe: string theory. Originally conceived as a way of explaining the forces inside atomic nuclei, it soon morphed into a framework for quantum gravity. Theories of quantum gravity seek to gain new insights into the universe by unifying general relativity, which describes gravity and the physics of the very big, and quantum mechanics, which governs the physics of the very small.
Knotty problems
By the 1990s, string theory had become one of the leading contenders for such a theory of everything. Instead of a universe made of fundamental particles, string theory describes one built from unimaginably tiny strings that vibrate in 10 dimensions, nine of space and one of time. To make the theory tally with the three spatial dimensions and one of time that we observe in the universe, the extra spatial dimensions of space have to be “compactified”, curled up so small as to be undetectable. Each method of compactification leads to a different universe. The big challenge was to find the unique solution that describes our particular space-time.
This effort ran into a problem. The universe that we appear to live in, with dark energy represented by a small, positive cosmological constant, is known as a de Sitter space-time. And for all its promise, physicists struggled to use string theory to build such a universe using the simplest ways of compactifying extra dimensions.
Then, in 2003, Shamit Kachru, Renata Kallosh, Andrei Linde and Sandip Trivedi (together nicknamed KKLT) way to construct our sort of space-time from string theory. Their work was hailed as a triumph for the theory, but it came at a huge cost.
String theory works at high energies, of the kind that existed moments after the big bang. To describe some particular space-time at today’s lower energies, string theory must be used to find a so-called effective field theory. The exact space-time you get using the KKLT construction depends on precisely how the extra dimensions are compactified and how magnetic and electric fluxes are threaded through these geometries. And by 2005, string theorists showed that this could be done in at least 10500 ways, each giving us a different viable de Sitter space-time. The result was a sprawling landscape of potential universes, a multiverse in which every conceivable space-time can exist. Although KKLT proposed a way to build an effective field theory that describes a de Sitter space-time, it couldn’t deliver an exact theory for our own.
Enter the Swampland
This fact troubled Cumrun Vafa, a string theorist at Harvard University. Not because he found the landscape problematic: “I didn’t have any allergic reaction to that,” he says. Rather, he was unhappy with the KKLT construction itself. Besides not producing the desired result, he says that the KKLT proposal was too mathematically complex to verify: others had to take it on trust that the method worked.
Vafa began to look at the question the other way round, asking whether all possible effective field theories can emerge from string theory, or whether string theory forbids certain varieties, and hence certain types of universes. He realised that, if string theory wanted to remain in contention as a theory of everything, it should outlaw effective field theories that fail to accurately describe our universe once gravity is introduced, a common failing. Such variants should be instantly relegated to a forbidden patch of the string landscape. Vafa christened this patch the Swampland, a slushy bog of untenable ideas.
“We may end up with a new universe that can’t be described in the language of our current universe”
The Swampland idea lay dormant for a decade, says string theorist Eran Palti at the Max Planck Institute for Physics in Munich, Germany. Then, in March 2014, cosmologists using a telescope at the South Pole called BICEP2 unintentionally brought it back into focus. They claimed to have seen evidence of primordial gravitational waves generated by inflation, the exponential expansion of space-time thought to have happened in the first fractions of a second after the big bang. This would have represented the first sighting of ripples in the fabric of space-time, a prediction of Einstein’s general relativity. Cosmologists celebrated. But string theorists were stymied. Their theory couldn’t generate such gravitational waves.
In particular, string theory models capable of explaining BICEP2’s gravitational waves had the seeming side effect of stopping inflation prematurely. “Primordial gravitational waves of this magnitude are in strong tension with string theory,” says Palti. In other words, the effective field theories that predict them may reside in the forbidden Swampland.
Then, in January 2015, the BICEP2 researchers retracted their claim. The signals they thought were due to gravitational waves were the result of dust in the Milky Way that they hadn’t properly accounted for. The fiasco, however, was good news for some string theorists. It showed that their theory had been right to call such results impossible. Vafa’s Swampland conjecture had passed a big test. “This led to a revival of his idea,” says Palti.
Then Vafa proposed something that gave the conjecture yet another shot in the arm. “What happened last summer was kind of amazing,” says Andrei Linde of Stanford University in California.
After nearly two decades of string theorists failing to construct any simple models of de Sitter space-time, Vafa wondered whether such a thing might actually be impossible. In what he calls the de Sitter conjecture, he and his collaborators boldly speculated that all effective field theories capable of describing a universe where dark energy is a cosmological constant belong to the Swampland. A de Sitter universe can’t be a solution to the equations of string theory.
For Linde, the de Sitter conjecture is just that, a conjecture, an unproven explanation. Until it is shown to be correct, he is standing by the KKLT construction and its promise that a universe with a cosmological constant can be described by string theory. “It’s a complicated story,” he says. “One should not, on the basis of arguments which are not proven, suddenly abandon what was done before.”
The de Sitter conjecture “may or may not be correct”, agrees Vafa. “We’ll find out when we study it more.” If proved correct, it has major implications for the standard model of cosmology. Not least among these, according to Vafa and others, is that it suggests a dark energy density that instead of being, to a first approximation, constant, is slowly decreasing with time.
If so, that would have profound consequences, says string theorist Timm Wrase at the Vienna University of Technology in Austria: “It certainly has huge implications for the fate of the universe.” Over the coming tens of billions of years, dark energy may go to zero, or even become negative. “And then maybe the universe would end in a big crunch, instead of expanding forever.”
Such a form of changing dark energy is called quintessence. The idea was quite popular before the cosmological constant became the flavour du jour.
Linde was one of the first to work on models of quintessence, but he is unconvinced. “Quintessence is possible, but it brings more problems than it can solve,” he says.
Except the universe may be moving in that direction. Over the past few years, hints have emerged that a changing density of dark energy may actually solve a surprising cosmological conflict.
The conflict arises from two different ways of measuring the present-day expansion of the universe, a factor known as the Hubble constant, H0. One method involves measuring it directly by studying stars and supernovae in nearby galaxies. The other involves examining the cosmic microwave background, the universe’s first light that was emitted about 380,000 years after the big bang, and then extrapolating from that data to the present-day universe. The two methods generate significantly different results.
The big twist
While the discrepancy could be due to experimental error, it could also be resolved by with time, treating it as a form of quintessence.
You might expect string theorists following Vafa’s ideas to be rejoicing at the news. But they aren’t. “The tension in H0 and the de Sitter Swampland conjecture go in opposite directions,” says Wrase. Whereas the de Sitter conjecture requires the dark energy density to get smaller with time, the Hubble constant problem is resolved only if this density increases.
As for the fate of the universe, an increasing dark energy density suggests that a big rip, rather than a big crunch, lies in store. “That’s the horror-show version,” says Adam Riess at Johns Hopkins University in Maryland, a leader of one of the teams studying the Hubble constant. Eventually, there would be so much dark energy in each bit of space-time that its repulsive force would shred everything: galaxies, planets, molecules, atoms and, eventually, space-time itself. “Resisting dark energy would be futile,” he says.
So we are back to square one, seemingly, with conflicting ideas suggesting dark energy is decreasing, staying constant or increasing with time, and the fate of the universe on the line. And that is where Vafa believes there might be a way of reconciling the Swampland conjecture with the H0 discrepancy.
Alongside dark energy, another invisible component of the universe is dark matter, a substance whose gravity is thought to be holding galaxies and clusters of galaxies together. If dark energy is losing strength, says Vafa, this will have an impact on dark matter. “String theory tells you that there should be an interaction.” He and his colleagues have found that the interaction causes the mass of dark matter particles to decrease over time. And this changes the extrapolated value of the Hubble constant, causing the discrepancy to shrink. “We were not trying to resolve the H0 tension, but it reduced it nevertheless,” he says. “That’s quite a non-trivial thing.”
Does this mean we are heading for a big freeze after all, rather than a big crunch or a big rip? Not quite. Look closer, and the consequences of Vafa’s ideas make all other scenarios look tame. It implies that, tens of billions of years from now, the universe will be radically transformed. “What that typically means in string theory is that a new dimension opens up. So it’s a completely new universe, which is not describable in terms of the language of our current universe,” he says. “We now live in three space dimensions. In this new theory, it might be four spatial dimensions, for example.”
Any such new spatial dimension would be the result of one of string theory’s extra dimensions suddenly springing free from its compactification. The universe resulting from this big twist would be nothing like our own. “A completely new phase takes over,” says Vafa. So, while the universe continues to exist, it is unclear what properties it will have and what its subsequent trajectory will be. “More details need to be known to say what may happen,” says Vafa. “We have no way of knowing accurately what this new phase may look like.”
A slew of proposed experiments may help resolve the debate, by tightening the bounds on the nature of dark energy. String theorists will be watching closely. After decades of being accused of not making any testable predictions, they could be close to coming up with some, if only in broad brushstrokes. For example, if string theorists can prove the de Sitter conjecture, it would lead to a prediction that the sort of space-time favoured by conventional cosmology can’t possibly exist. But then if experiments find indisputable evidence supporting the cosmological constant and a de Sitter vacuum for our universe, says Palti, “we can say string theory is wrong”.
Whatever happens, the universe’s future looks anything but boring.
