As powerful as inflation theory seems to be at solving many mysteries of creation, it may still have a fundamental problem at its heart: The dreaded singularity. One possible way around the singularity problem simply is to assume that there was no ultimate origin of the universe, or of the multiverse. In this view, if one were to run the movie of cosmic evolution in reverse, everything would not suck back down into an infinitely dense, infinitely tiny spec. Cosmic evolution simply would extend infinitely into the past. But Turok finds this explanation just as unsatisfying as the singularity itself. After all, arguing that the cosmos is infinitely old is no more illuminating than saying the universe began in a singularly enigmatic spec in which all the laws of physics break down.
And so Turok has been searching for an alternative explanation. His search builds on work begun in the early 1980s by Hawking and Jim Hartle, a cosmologist at the University of California, Santa Barbara.
In 1983, Hartle and Hawking used a mathematical approach called the “path integral” to calculate the odds that the universe had begun in a variety of different ways. In a sense, Turok says, this approach “uses the laws of physics to define their own starting point.” What emerged was a proposal dubbed the "no-boundary" hypothesis. It can be imagined with a little help from a simple geometric shape: a cone.
Imagine that the cone represents the evolution of the universe. Time runs up the side of the cone. Space runs around the cone. As you go up ( forward in time), the width of the cone (space) enlarges. The origin of time and space is the point at the bottom. In the traditional big bang model, this is the singularity.
But in quantum physics, there is no such thing as a precise point — there is an uncertainty to it. To visualize this, imagine that the point is rounded off. (Picture an extreme blow-up of the tip of a ball point pen.) This is just what Hartle and Hawking’s path integral predicted as the most likely configuration for the universe at its birth. Rather than the time dimension (up the side of the cone) beginning at a discrete point, it emerges from the space dimension (around the cone). And just as there is no point on the surface of a sphere like the Earth where one can say the sphere “begins,” there is no distinct point on the hemispherical, rounded-off bottom of the cone where time or space begins. There simply is no starting point, and there is no distinction between space and time — or even past and future.
In essence, Hartle and Hawking proposed that the universe inflated out of the bottom of the cone and then experienced the big bang. But there was one problem: Hartle and Hawking could complete their path integral calculations using a class of inflationary theories that produced only a closed universe. Because current observations suggest that the universe is either open or flat, the Hartle-Hawking creation model leads to a different kind of universe than the one we live in.
There the no-boundary idea lay until 1998, when Turok began meeting with Hawking for tea-time chats about models of inflation that could produce an open universe. Turok had been searching for an open inflation theory since the mid-1990s. Working with Martin Bucher of Cambridge and Alfred Goldhaber of the State University of New York at Stoney Brook, Turok and his colleagues had found that a double dose of inflation could have done the trick.
The double-dose theory goes like this: First, as in traditional inflation, scalar fields temporarily get stuck at high potential energy, causing a patch of spacetime to nucleate a bubble of false vacuum. This bubble inflates. As the potential energy of the fields begins to decay, the fields then get stuck for a second time. Now, a bubble of false vacuum forms within the first bubble and inflates — a second bout of inflation. Bizarrely enough, calculations show that the space inside this second inflating bubble, which corresponds to our universe, is geometrically open.
But as Turok points out, this scenario is just too “baroque.” Moreover, it doesn’t describe where the first inflation-driving fields came from (the initial conditions), nor why they should have gotten stuck a second time to create a second bout of inflation.
Over tea, Hawking suggested that it might be possible to solve these problems by modifying the no-boundary idea he had developed with Hartle to produce an open bubble universe with only one bout of inflation. Such a theory would vastly simplify things and explain the initial conditions for inflation — meaning no less than the initial conditions of the universe itself.
“This was a genuine surprise,” Turok says. He decided to take up Hawking's challenge.
Turok's first attempt at a solution was disappointing, he says, because the path integral approach seemed to rule out open inflation from the Hartle-Hawking no-boundary "cone." The reason: Infinite amounts of energy would be produced.
“When I brought this up with Stephen, he said, ‘wait, you didn’t include the gravitational energy,’” Turok recalls.
Once again, since energy is equivalent to mass, energy exerts a gravitational field. Gravity, in turn, has a special feature: It’s energy is negative. In other words, infinite positive energy would produce a perfectly balancing infinite negative energy. Crank this into the calculations, Turok and Hawking then realized, and the no-boundary model would produce an open, inflating universe — and without any fancy double inflation. In fact, the path integral calculations showed that such a universe was the most likely universe.
NO POD FOR THIS PEA
What does this new creation model look like? Turok and Hawking had
imagined it using math. But when Turok attempted to describe the work for
an article in the English newspaper the Sunday Times, the journalist asked
him for a physical description. “You must think of something we can picture,”
the reporter insisted.
“Well it's small and round, but not perfectly round, and it has little dimples — it's something like a pea,” Turok replied.
The reporter jumped on this and said, "okay, it's a pea,” Turok recalls.
A very special pea to be sure. It's a millionth of a trillionth of a trillionth the size of a pea. But it's a lot denser than ordinary matter, so its mass actually is about that of a pea. Space and time are blended together in the pea such that its “bottom” half is just like the rounded-off tip of the cone in the original Hartle-Hawking no-boundary model. Here again, time emerges from the geometry of space and there is no discrete beginning to either.
When Turok and Hawking worked out the calculations describing this remarkable creationary object, they found to their astonishment that an open inflating universe instantly (thus the name "instanton") sprouted out of the "top" of the pea.
Those little dimples on the surface of the pea that Turok had described to the reporter aren't there for nothing. They actually are a physical representation of quantum fluctuations that would have ruffled spacetime. And when the pea instanton sprouts into a universe, these imperfections form a kind of cosmic pattern on which the tapestry of the universe is woven.
The universe, Turok concludes with wonderment, “all comes out of one formula in a beautiful way.”
For Turok, part of the formula’s beauty lies in its sheer simplicity and economy. “For sure, I think this is the simplest way for starting the universe,” Turok says. And for him and many other scientists, simplicity and economy are major virtues. These qualities also seem to be the trend in fundamental physics. “The farther one goes back in time, the hotter the universe gets,” he says. “And there is strong evidence that things get simpler and simpler at higher and higher energies.” Because of this increasing simplicity the farther back in time one probes, it is now theoretically possible to describe all the fundamental phenomena of nature in an equation that fits on one line — albeit, a rather long one!
This has a profound implication: If we probe close enough to the origin of space and time, the equations that physicists use to describe the laws of nature may become so simple that it may become possible to write them on far less than one long line. They might even fit on a T-shirt. In fact, Turok claims that one extremely simple equation might do the trick: “We may be able to devise a single symbol that contains all the laws of nature.” This would be, in fact, the holy grail of physics: a theory of everything from which all the laws of nature can be derived.
But the multiverse theory, Turok notes, runs counter to the trend of
increasing simplicity in physical explanations for the origin of the universe.
The multiverse is a profoundly complex entity. In fact, its proponents
state that the laws of physics likely would be different in each branch
of the tree. This means that it would never be possible to understand how
other parts of the multiverse worked — and it would never be possible to
derive a single, economical theory of everything, Turok argues.
And so his preference is for what he calls a “one-shot” universe with
“one beginning and one big bang.” A universe exactly like the one produced
by the pea instanton.
But some cosmologists say there are fatal flaws in Turok and Hawking’s
beloved instanton. To begin with, critics say the Cambridge scientists
have not eliminated the singularity entirely: It survives as a single point
inside the primordial instanton.
There are other criticisms as well. Linde points out that the pea instanton
gives rise to a universe that is too open. The density of matter
is so low, in fact, that galaxies would be few and far between; even using
the Hubble Space Telescope, we wouldn’t be able to see another galaxy from
our own.
Moreover, in explaining how the universe could have come from nothing, the pea instanton uses the idea of “quantum tunneling,” Linde says. In the mathematical language of quantum physics, quantum tunneling describes how a particle or a field can move from one side of a seemingly insurmountable barrier to the other without actually passing over or through the barrier in a classical sense. The way Linde sees it, Turok and Hawking’s instanton describes the origin of the universe as a quantum tunneling event from a state of nothingness to a state of existence.
“This is like creating a hydrogen atom from nothing. I cannot justify it. I cannot understand it,” Linde laments.
THE UNIVERSE JUST IS
Turok replies that Linde misunderstands what he and Hawking have done.
“It's not tunneling,” Turok insists. The pea instanton is not, in fact,
created from nothing. “Nothing” simply has no meaning in this context.
The instanton, meaning the universe at its birth, just is. In essence,
the theory shows how the laws of physics make its existence inevitable.
“It really is a rather unique thing and I don’t think this is widely understood,” Turok says.
As to the pea instanton universe being too open, Turok agrees. But he remains undaunted. “The fact that it’s wrong by a factor of 30 is encouraging because the calculation was done with a very simple model and yet it’s not that far wrong.” So for Turok, the fact that the pea instanton universe is too open is simply cause for further tinkering.
Finally, the surviving singularity within the instanton is, in his words, “so mild that, like the singularity in the electric field in the center of a hydrogen atom, one can still calculate the quantum properties of the universe without any ambiguities.” He points out that “there are singularities within black holes, yet we don’t doubt that black holes exist.” So just because there is a singularity within the instanton doesn’t mean that the entire model should be tossed out. “The presence of a singularity simply says you don't know what you're doing there,” Turok says. “It’s still possible that the physics away from the singularity is fine.”
“I like to say that what we've done is sidestep the singularity rather than avoid it altogether,” Turok concludes. “We've found a way to go back to the beginning of time and go around the singularity.”
Time will tell whether he and Hawking have succeeded. Two new satellites, NASA’s MAP mission and the European Space Agency’s Planck Surveyor, scheduled for launch early in the next century, should be able to test their theory by looking for evidence of the quantum fluctuations — the dimples — predicted by the pea instanton theory.
Of course, even if Turok and Hawking are onto something with their pea instanton, it would still leave a very fundamental question unanswered: How did the pea get there? Turok and Hawking say it's meaningless to ask the question. There is no “outside” of the pea, no “before” the pea. It just is, an object implied by the very laws of physics. But what created those laws?
Says Turok: “We don't know how to create physics from nothing.”