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In his last paper on cosmology, Stephen Hawking and a younger colleague attacked cosmic inflation and its discontents.

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Stephen Hawking’s (almost) last paper: putting an end to the beginning of the universe

When Stephen Hawking died on 14 March, the famed theoretical physicist had a few papers still in the works. Today, the Journal of High Energy Physics published his last work in cosmology—the science of how the universe sprang into being and evolved. (Other papers on black holes are still being prepared.) In the new paper, Hawking and Thomas Hertog, a theoretical physicist at the Catholic University of Leuven (KU) in Belgium, attempt to stick a pin in a bizarre concept called eternal inflation, which implies—unavoidably, according to some physicists—that our universe is just one of infinitely many in a multiverse. Borrowing a concept from string theory, Hawking and Hertog argue that there is no eternal inflation and only one universe. But what they’re driving at is something even more basic: They’re claiming that our universe never had a singular moment of creation.

How does the argument work? Follow its winding thread to the end of the beginning.

Let’s start with the basics: What is cosmic inflation?

Cosmic inflation is a monumental growth spurt that supposedly stretched the infant universe during the first tiniest fraction of a second. Dreamed up in 1979 by American theorist Alan Guth, inflation holds that just after the big bang, space stretched exponentially, doubling the size of the universe again and again at least 60 times over before slowing dramatically.

Why would cosmologists believe in something so bizarre?

Inflation solves a major puzzle: Why is the universe so uniform? For example, space is filled radiation lingering from the big bang, the cosmic microwave background (CMB). It has almost exactly the same temperature everywhere in the sky. That’s odd, as widely separated points seem at first glance to be too far apart for any influence to reach from one to the other over the 13.8 billion years the universe has been around. Inflation solves that puzzle by implying that all the points in the sky started out close enough to interact, and then were stretched far apart.

Is that all inflation does?

Ironically, inflation also does a great job of explaining why the universe isn’t completely uniform. Obviously, space is studded with galaxies. According to the theory, inflation stretched infinitesimal quantum fluctuations in those first moments to extragalactic size. The fluctuations then produced variations in the dense soup of fundamental particles that seeded the formation of the galaxies. Inflation predicts a particular spectrum of longer and shorter fluctuations. Strikingly, studies of the CMB and the galaxies confirm that distribution. 

Cosmic inflation posits that the infant universe underwent a mind-boggling growth spurt, instantly stretching subatomic ripples to the cosmic scale.

WMAP Science Team/NASA

So what’s eternal inflation?

Here’s where the concept of inflation runs into problems of its own. Physicists deeply dislike the idea that inflation would stop suddenly, for no particular reason. They’d much rather have a mechanism that explains what drove inflation and then caused it to stop. That’s why they assume some sort of quantum field drove it, before petering out. The idea is that the field starts out in an only approximately stable, higher-energy “false vacuum” state in which space stretches exponentially. It then relaxes to its true lowest energy state, in which space expands much more slowly.

The scenario works a little too well, however. The exponentially expanding false vacuum produces more and more of itself, so there’s ever more space expanding at an incredibly fast rate. Our universe is a patch that has undergone the transition to the low-energy true vacuum state. But such transitions should happen randomly, so there should be lot of other universes, too. In fact, the process should produce an ever-increasing amount of space that’s growing at an exponential rate, peppered with an infinite number “pocket universes” growing more slowly.

Is that a problem?

It depends on whom you ask. At the most basic level, the existence of all these other universes wouldn’t affect our universe. They’re just too far away to have any connection with ours. On the other hand, the notion of eternal inflation and a multiverse may thwart cosmologists’ entire enterprise of explaining why the universe is the way it is, Hertog says. Things like the values of certain key physical constants could vary randomly among the pocket universes, he says, which would render moot any effort to explain why they have the values they do in our universe. They would be set by random chance, Hertog says, and that’s not very satisfying.

So how does Hawking’s and Hertog’s paper solve the problem?

Hawking and Hertog argue that, in fact, eternal inflation does not occur. To do that, they borrow a concept from string theory that enables them to equate two different types of theories with different dimensionalities. In 1997, Argentine-American theorist Juan Maldacena considered a volume of space in which gravity was at work. Maldacena, who is now at the Institute for Advanced Study in Princeton, New Jersey, then demonstrated that theory was equivalent to an easier-to-work-with quantum theory on the boundary of the space that didn’t include gravity. It’s like saying whatever goes on inside a can of soda can be captured by a theory describing only what’s happening on the can’s surface.

Eternal inflation emerges because, in the very early universe, the quantum fluctuations in the field that drives inflation are as big as the field’s average value. But Hawking and Hertog argue that under those conditions one cannot simply carry on with Albert Einstein’s general theory of relativity, but instead must use a maneuver like Maldacena’s to view the entire situation in a space with one less dimension. In that alternative space, things are more tractable, they claim, and the physics does not lead to eternal inflation. Instead, a single, well-behaved universe merges.

So what does this have to do with the beginning of the universe?

That’s where things get interesting—and tricky. The concept of equating one theory to another in a space with one fewer dimension is known to theoretical physicists as holography. In his work, Maldacena equated one theory to another in a space with one less spatial dimension. But, Hertog argues, the principle of holography allows theorists to jettison the dimension of time, instead. So in Hawking’s and Hertog’s theory, through the principle of holography, the very early universe should be described by a theory with just three spatial dimensions and no time.

But why would you want to get rid of time?

Ever since it became clear that the universe had a beginning, the moment of its birth has been a headache for theorists. Roughly speaking, Einstein’s general theory of relativity does a fine job of explaining things after the moment of the big bang, but cannot handle the instant of creation itself. That moment forms a “singularity” in spacetime—like a mathematical function that explodes to infinity—that trips up the theory. So theorists have long sought a way of avoiding that singularity—and losing time would be one way to do that.

It’s a problem that fascinated Hawking his entire career, Hertog says. Decades ago, he suggested an alternative fix by speculating that in the very beginning, time was, crudely speaking, dimensional, an idea that doesn’t mesh with the new work.

So is this the end for eternal inflation and the big bang singularity?

Probably not. Others will scrutinize Hawking’s and Hertog’s invocation of the dimension-changing relation. And even if other researchers find it to be sound, there’s still a major question to be answered, Hertog acknowledges. If theorists start with a theory with only spatial dimensions, how does time finally emerge from it? “We threw out a new paradigm,” Hertog, says, “but there's a lot of work to be done.”

*Correction, 3 May, 10 a.m.: This story has been updated to correct the name of the Institute for Advanced Study.