Universe is Finite, "Soccer Ball"-Shaped, Study Hints

Studying the cosmic background radiation
of deep space, French cosmologists and
an American mathematician suggest that
space may be finite and shaped
like a dodecahedron (above).

Illustration courtesy Jeffrey Weeks

What is the shape of the universe? The question has tantalized humankind since civilization first gazed toward the heavens.

Theories about whether space is finite or infinite, flat or curved have blazed in the firmament of scientific discourse with varying intensity over time, burning brighter or fading in the face of new data and competing ideas.

Now a new study of astronomical data only recently available hints at a possible answer: The universe is finite and bears a rough resemblance to a soccer ball or, more accurately, a dodecahedron, a 12-sided volume bounded by pentagons. A new study of cosmic background radiation data only recently available hints that the universe is finite and bears a rough resemblance to a soccer ball.

If proven by further evidence and scrutiny, the model would represent a major discovery about the nature of the cosmos.

"What makes it exciting now is it's not a matter of idle speculation," said Jeffrey Weeks, a freelance mathematician in Canton, New York, and study co-author. "There's real data to look at and the possibility of getting a definite answer."

Weeks, recipient of a MacArthur Fellowship or so-called "genius award," arrived at the model with a team of French cosmologists while studying cosmic background radiation observed by NASA's Wilkinson Microwave Anisotropy Probe (WMAP).

With a microwave antenna pointed into deep space and shielded from local interference emanating from the sun, Earth, and moon, the spacecraft has recorded the clearest soundtrack to date of the microwave radiation echo of the Big Bang, the event most scientists believe created the universe.

Cosmic Afterglow

Like the visible light of distant stars and galaxies, cosmic background radiation allows scientists to peer into the past to the time when the universe was in its infancy. Density fluctuations in this radiation can also tell scientists much about the physical nature of space.

NASA released the first WMAP cosmic background radiation data, collected since October 2001, in February.

Combing through those observations, Weeks and his colleagues found that the most telling information supplied by WMAP was, in fact, the resounding echo of what was missing. Density fluctuations on the largest scale were far weaker than expected, a gap Weeks and colleagues say is best explained by a finite universe.

To illustrate the concept, Weeks points to the analogy of an ocean and a bathtub. While the ocean (an infinite universe) can support 40-foot-long waves, a bathtub (the finite universe) is simply too small. The bathtub cannot support waves longer than the length of the tub itself.

Moreover, observations of the cosmic background radiation enabled Weeks and his colleagues to posit possible shapes for the universe to explain its fluctuating density. The researchers could then test their models through mathematical proofs against the microwave data gathered by the WMAP satellite.

Among cosmologists, three broad categories vie as the most likely shapes to fit the cosmos: flat, negatively curved (saddle-shaped), and positively curved (spherical) space.

But Weeks said the discovery of dark energy in 1998, a little-understood force found in the vacuum of space, make models for negatively curved space more difficult to reconcile with scientific observations. Meanwhile the shape of flat universe models, Weeks said, imperfectly fit the mathematical proofs derived from WMAP cosmic background radiation recordings.

Think Positive

So Weeks said he started with the simplest model of a finite space, a torus.

(To picture a torus, roll up the sides of a piece of paper to create a cylinder. Starting over, roll the paper top to bottom to create a new cylinder. Now imagine rolling both ends simultaneously, but instead of using paper—two-dimensional space—start with the rectangular space of your office or living room—three dimensional space.)

"When you actually go and do the computation and you say, what sort of microwave sky do you expect to see in a torus universe, it doesn't match very well," said Weeks.

"But the good news then is that…if you start with a dodecahedral block of space and again hook up on the sides, then it matches quite well."

In other words, taking the density fluctuations in cosmic background radiation recorded by WMAP, the math adds up if the universe is finite and shaped like a dodecahedron.

Weeks cautions that his team's model of a finite, dodecahedral-shaped universe, while promising, is hardly a proven theory. "There's more work to be done, he said. "It could be affirmed, or it could be refuted."

A description of their research appears tomorrow in the science journal Nature.

In an accompanying perspective article, George F. R. Ellis, a mathematician at the University of Cape Town, South Africa, writes that the researchers' cosmic map "accounts for the WMAP data better than do standard models," he wrote.

"Can this proposal be confirmed? Yes indeed," Ellis wrote, noting that future observations from WMAP's successor, a European satellite to be launched in 2007 even more accurate than its NASA counterpart, will provide key observations on cosmic background radiation that could confirm or disprove Weeks' theory.

Ellis concluded: "The WMAP data, as interpreted by [Weeks and colleagues], suggest that we might indeed live in such a small closed universe."

Cosmic Soccer Ball? Theory Already Takes Sharp Kicks


Published: October 9, 2003, NY Times

In an unusual logjam of contradictory claims, a revolutionary new model of the universe, as a soccer ball, arrives on astronomers' desks this morning at least slightly deflated.

In a paper being published today in the journal Nature, Dr. Jeffrey Weeks, an independent mathematician in Canton, N.Y., and his colleagues suggest, based on analysis of maps of the Big Bang, that space is a kind of 12-sided hall of mirrors, in which the illusion of infinity is created by looking out and seeing multiple copies of the same stars.

If the model is correct, Dr. Weeks said, it would rule out a popular theory of the Big Bang that asserts that our own observable universe is just a bubble among others in a realm of vastly larger extent. "It means we can just about see the whole universe now," Dr. Weeks said.

But other astronomers, including a group led by Dr. David Spergel of Princeton, said a continuing analysis of the same data had probably already ruled out the soccer ball universe. They promised to post their results soon on the physics Web site arXiv.org/list/astro-ph.

"Weeks and friends are making a dramatic claim, perhaps one of the biggest science stories of the century," said Dr. Neil Cornish, a physicist at Montana State University, "but extraordinary claims require extraordinary support."

For now, the two groups, who have been in intense communication the last few days, disagree on whether the soccer ball universe has been refuted. What is amazing about this debate, they all agree, is that it will actually be settled soon, underscoring the power of modern data to resolve issues that were once considered almost metaphysical.

"This is what got Giordano Bruno burned at the stake," said Dr. Max Tegmark, a cosmologist at the University of Pennsylvania. "Is space infinite or not?"

In Nature, Dr. Weeks and his colleagues write: "Since antiquity, humans have wondered whether our universe is finite or infinite. Now, after more than two millennia of speculation, observational data might finally settle this ancient question." The other authors are Dr. Jean-Pierre Luminet of Paris Observatory; Dr. Alain Riazueleo of the French atomic energy center CEA, in Saclay, France; Dr. Roland Lehoucq of the Paris Observatory and CEA; and Dr. Jean-Phillippe Uzan of the University of Paris.

The evidence for and against a finite universe resides in a radio map of the baby universe produced last February by a NASA satellite, the Wilkinson Microwave Anisotropy Probe. It shows that 400,000 years after the Big Bang, the event in which space and time emerged, the universe was laced with faint waves and ripples, which are the origin of modern galaxies and other cosmic structures. In an infinite universe, according to theory, waves of all size should appear in the sky, but in the Wilkinson data there was a cutoff: no waves larger than about 60 degrees across appeared in the sky.

If the universe were a musical instrument, it would be inexplicably missing its low notes, perhaps, some cosmologists have suggested, because it is too small to play them. The universe is finite rather than infinite, they speculate. Like a violin that cannot produce deep cello notes, the universe cannot produce waves larger than itself.

In such a universe, if you went far enough in one direction, you would find yourself back where you started, on the other side of the universe, like a cursor disappearing off the left side of a screen and reappearing on the right.

One simple example of this is a torus, or a bagel shape, which is what you get when you wrap the left and right and top and bottom sides of the screen around so that they meet.

In the Nature paper, Dr. Weeks and his colleagues propose that three-dimensional space has 12 sides, like a soccer ball, or more technically a dodecahedron. This model would fit with the cutoff of large waves observed in the Wilkinson satellite data. Each face is "glued" to its opposite number. (Don't try this at home.) A spaceship crossing one face or panel of the soccer ball would enter the other side of the ball. After traveling 74 billion light-years it would find itself back where it had started.

While the lack of cosmic low notes is suggestive, cosmologists say there is a definitive test of finite universes in the Wilkinson map. When the cosmic radiation intersects the edges of the universe, it would make identical circles, like a balloon squashed in a box, on opposite sides of the sky. In the case of a bagel, there would be two circles in the map, on opposite sides of the sky. In the case of Dr. Weeks's dodecahedron, there would be six pairs of circles, each about 35 degrees in diameter.

"This is a much higher bar to clear," Dr. Cornish said.

Dr. Tegmark said: "What's nice is it's so testable. It's the truth or it's dead. The data is even out there, on the Internet. It's just a question of sifting through it."

But so far the circles have not showed up.

Earlier this year, Dr. Tegmark and his wife and colleague Dr. Angelica Oliveira-Costa, Dr. Mattias Zaldarriago, of Harvard, and Dr. Andrew Hamilton of the University of Colorado, searched the Wilkinson data for oppositely matched circles. The results, they said, ruled out the possibility that the universe was shaped like a bagel, no doubt disappointing New Yorkers who would like to have imagined a cosmic connection with their breakfast.

Dr. Tegmark said that the results also ruled out Dr. Weeks's dodecahedron. "We ought to have seen those circles in our study," he said.

Meanwhile, a more thorough analysis of the data, looking for all possible circles, has been undertaken by Dr. Spergel, who was part of the original Wilkinson team, Dr. Cornish, and Dr. Glenn Starkman of Case Western Reserve University in Cleveland. The study, about two-thirds complete, had already eliminated many simple models of so-called "small universes," including a dodecahedron when the Nature paper hit their desks last week, Dr. Spergel said.

"No soccer ball, no doughnuts, no bagels," he said.

But Dr. Weeks said there were potential gaps in the circle search methods. For one thing, if the dodecahedron were slightly larger, he said, the circles would be smaller and would not show up in Dr. Spergel's search. But until all the papers are posted on the archive or published where everybody can read them, these claims cannot be evaluated.

Dr. Weeks said that astronomers from both teams would join this fall to test the circle search, using simulated data. If the models are false, they could be ruled out as early as November, he said.

Dr. Cornish said that, although it was the scientific community that would ultimately decide, his team was confident of its results. "I don't see any wiggle room," he said.

But because it is such a "truly spectacular claim," he said, they are planning in the next few days to run a special test focused on the particular model. The test could detect very small circles. "We can push it to where there's no chance," Dr. Cornish said.

The prospects for the finite universe, he added, look bleak.

The stakes for cosmology, should the soccer ball or some other variety of small universe prevail, are not small at all. A small universe, everybody agrees, would present severe problems for the prevailing theory of the Big Bang, known as inflation, which posits that the cosmos underwent a burst of hyperexpansion in its first moments.

Moreover, Dr. Weeks said, a small universe would eliminate one popular variant of the theory known as eternal inflation, in which bubble universes give rise to one another endlessly in what some cosmologists call a "multiverse."

"This puts the whole universe in view," he explained. "It wouldn't rule out other universes. There could be others. They would be totally unrelated, without any contact between them."