Universe as Doughnut: New Data, New Debate
March 11, 2003
By DENNIS OVERBYE
Some scientists say new data hint that space is like a hall of mirrors in
which light travels around a small universe, creating
an apparently endless chain of images.
Image by Dr. Max Tegmark, University of Pennsylvania
Long ago in the dawn of the computer age, college students
often whiled away the nights playing a computer game called
Spacewar. It consisted of two rocket ships attempting to
blast each other out of the sky with torpedoes while trying
to avoid falling into a star at the center of the screen.
Imagine that the Spacewar screen is wrapped
around to form a cylinder or a section of a doughnut so
that the two edges meet.
Although cartoonish in appearance, the game was amazingly
faithful to the laws of physics, complete with a
gravitational field that affected both the torpedoes and
the rockets. Only one feature seemed outlandish: a ship
that drifted off the edge of the screen would reappear on
the opposite side. |
Real space couldn't work that way.
Or could it?
That is the picture of space, some cosmologists say, that
has been suggested by a new detailed map of the early
universe. Their analysis of this map has now provided a
series of hints - though only hints - that the universe may
have a more complicated shape than astronomers presumed.
Rather than being infinite in all directions, as the most
fashionable theory suggests, the universe could be
radically smaller in one direction than the others. As a
result it may be even be shaped like a doughnut.
"There's a hint in the data that if you traveled far and
fast in the direction of the constellation Virgo, you'd
return to Earth from the opposite direction," said Dr. Max
Tegmark, a cosmologist at the University of Pennsylvania.
The new data have generated both buzz and skepticism among
cosmologists in recent weeks. Dr. Tegmark and other
astronomers agree that the measurements are far from
conclusive, or even persuasive about the shape of the
But if true, the doughnut universe would force cosmologists
to reconsider their theories about what happened in the
earliest moments after the universe was born in the Big
Bang; those theories predict an infinite cosmos.
The new findings have brought to center stage the hope that
astronomers may be able to test speculations about the
shape, or topology, of the universe that until recently
have been relegated to the abstract mathematical margins of
The results are part of the bounty of data produced by a
NASA satellite known as the Wilkinson Microwave Anisotropy
Probe, built and operated by an international collaboration
led by Dr. Charles L. Bennett of the Goddard Space Flight
Center in Greenbelt, Md. The satellite recorded the pattern
of heat, in the form of faint microwave radiation, that
fills the sky.
This radiation is believed to be the afterglow of the Big
Bang itself, and thus constitutes a portrait of the
universe when it was only 380,000 years old.
As the COBE satellite first confirmed in 1992, the
microwave cloud is laced with ripples and splotches - lumps
in the cosmic gravy - from which galaxies and other cosmic
structures would ultimately form.
According to theory, these lumps are born as microscopic
fluctuations during the first instant of time and then
amplified into sound waves as the universe expands and
matter and energy slosh around.
Now the new satellite has illuminated the findings of COBE
(pronounced KOE-bee, for Cosmic Background Explorer) in
By analyzing these waves cosmologists can determine many of
the characteristics of the universe, which scientists have
long debated, like its age and density. To their delight,
the first results from the Wilkinson satellite, released
last month, confirmed many of the strange ideas that
cosmologists entertained in the last decade, including the
notion that most of the universe consists of something
called dark energy, which is pushing space apart at an
"Cosmologists have built a house of cards and it stands,"
said Dr. James Peebles, a cosmologist at Princeton.
But to their even greater delight, perhaps, as they dig
into the trove released last month, cosmologists are
finding hints of even more strangeness.
In principle, in an infinite universe, the waves in the
cosmic fireball should appear randomly around the sky at
all sizes. But, according to the new map, there seems to be
a limit to the size of the waves, with none extending more
than 60 degrees across the sky.
The effect was first noted as a puzzle in the COBE data,
according to Dr. Gary Hinshaw, an astronomer at the Goddard
Space Flight Center and a member of the Wilkinson probe
team, and now seems confirmed.
If the universe were a guitar string, it would be missing
its deepest notes, the ones with the longest wavelengths,
perhaps because it is not big enough to sustain them.
"The fact that there appears to be an angular cutoff hints
at a special distance scale in the universe," Dr. Hinshaw
Another analysis of the new map suggests that there is a
special direction, as well as a special scale in the
universe. While reanalyzing the Wilkinson data to eliminate
radio noise from stars and our own galaxy, Dr. Tegmark, Dr.
AngM-ilica de Oliveira-Costa, also at Pennsylvania and
married to Dr. Tegmark, and Dr. Andrew J. S. Hamilton of
the University of Colorado have discovered that the
universe appears lumpier in one direction through space
than it does in another. When they combed finer variations
out of the map, the remaining large-scale variations formed
a line across the sky.
It could be a chance alignment, a statistical fluke, Dr.
Tegmark said, or contamination from radio noise from the
But in a paper posted on the physics Web site (at
arXiv.org/pdf /astro-ph/0302496) late last month, the three
cosmologists wrote that it was "difficult not to be
intrigued" that their results bore all the earmarks of what
are variously called small, compact, finite or periodic
If the universe is finite in one dimension, like a cylinder
or a doughnut, Dr. Tegmark said in an interview, there is a
limit to the size of clumps that can fit in that direction.
They couldn't be bigger than the universe in that
direction, just as a guitar string can only play a note so
low, depending on its length. So the biggest blobs would
have to squish out in a plane in other directions. The way
home around the doughnut would be perpendicular to that
Nobody is yet claiming that this is a revolution. The
notion of a special direction is on less firm ground than
the discovery of a cutoff of large structures. "More
detailed work in needed to clarify what's going on," Dr.
Dr. Martin Rees, a cosmologist at Cambridge University,"
said he didn't think there was evidence for "anything
crazy" in the data.
Even aficionados of finite universes are guarded. Dr. David
Spergel, a Princeton cosmologist and Wilkinson satellite
team member, called the results "intriguing," but
that they could also be due to chance.
Dr. Hinshaw called the findings of Dr. Tegmark's team
"surprisingly robust," but added, "I'm not sure it
something profound about the universe."
Dr. Alexei Starobinski, a theorist at the Landau Institute
in Moscow, proposed in 1984 with his mentor, Dr. Yakov B.
Zeldovich, that the universe could have been born as a
doughnut. Dr. Starobinski emphasized that an infinite
universe with ordinary Euclidean geometry was the most
natural universe and still favored by theory.
"However, theory is theory, but observations might tell us
something different," he said in an e-mail message.
The Science of Shapes
A Compact Universe
The new work involves topology, the branch of mathematics
that deals with shapes. Topologists are often accused of
not knowing the difference between a coffee mug and a
doughnut; because each object has one hole, the two can be
deformed into each other and are thus topologically
equivalent. In a similar vein, a figure 8 and a pair of
eyeglass frames are also the same to a topologist. The more
holes, the more complicated the topology.
The simplest topology is just the infinite space of the
Euclidean geometry taught in high school. But some
cosmologists have a hard time calculating how an infinite
universe could have appeared in that kind of space. Nature,
they contend, might have had an easier time making a small
"compact" universe than an infinite one, and they assume
Nature would take the easy way out.
"The basic idea is that God's on a budget," said Dr.
Smoot, a physicist at the University of California's
Lawrence Berkeley Laboratory and a leader on the COBE team.
The simplest of these compact universes is something called
a 3-torus, a doughnut wrapped in three different
dimensions. This object is essentially impossible to
visualize: it is the equivalent, in a way, of a cube whose
opposite sides are somehow glued together. In two
dimensions it works just like the Spacewar screen.
Living in such a universe would be like being inside a hall
of mirrors, Dr. Tegmark said. Instead of seeing new stars
deeper and deeper in space, you see the same things over
and over again as light travels out one side of your cube
and back in the other.
This mirror game is not limited to cubes and doughnuts.
Over the years mathematicians, particularly Dr. William
Paul Thurston, now at the University of California at
Davis, and Dr. Jeffrey Weeks, an independent mathematician,
have speculated about universes composed of various
polyhedrons glued together in various ways.
In 1996 the French astronomer Dr. Jean-Pierre Luminet of
the Paris Observatory and his colleagues Dr. Roland Lehoucq
and Dr. Marc Lachieze-Rey, both of the Center for
Astrophysical Studies in Saclay, France, developed a method
called "cosmic crystallography," using galaxy statistics
detect and diagnose the repeating periodic patterns that
would be created in the sky by light going around and
around in differently shaped universe.
Finite or Infinite?
Problems Are Posed
For Favored Theory
Why would the universe want to do this to us? Partly to
avoid the difficulties of the infinite, said Dr. Glenn
Starkman, an astronomer at the Case Western Reserve
University in Cleveland. Besides being difficult to create,
an infinite universe is philosophically unattractive. In an
infinite volume, he pointed out, anything that can happen
"Somewhere there are two guys having this same
conversation," Dr. Starkman said in a telephone interview,
"except that one of them has a purple phone."
Moreover, the idea that dimensions could be curled in loops
occurs naturally in theories that try to unite gravity and
particle physics, several physicists pointed out. For
example, according to string theory, the leading candidate
for a theory of everything, the universe actually has 10
dimensions - 9 of space and 1 of time - rather than the 4
we are familiar with. The extra dimensions are curled up
into submicroscopic loops, like the threads in an uncut
carpet pile, so that we don't notice them in ordinary life.
"This is the same idea on a very large scale," Dr. Smoot
Knowing that all nine of the spatial dimensions predicted
by string theory are finite and thus on the same footing
could help string theorists decide among the nearly endless
possibilities allowed by the theory, scientists say.
But a finite universe would create big problems for the
reigning theory of the Big Bang, inflation theory. It
posits that the universe underwent a burst of
hyperexpansion in its earliest moments. Among other things,
it implies that the observable universe today, a bubble 28
billion light-years in diameter, is only a speck on the
surface of a vastly greater realm trillions upon trillions
of light-years across.
"There's no natural way yet proposed to get the inflation
to stop and give a space that's big enough to house all the
galaxies but small enough to see within the observable
horizon," said Dr. Janna Levin, a Cambridge University
cosmologist who wrote about finite universes in her 1992
book, "How the Universe Got Its Spots, Diary of a Finite
Time in a Finite Space."
Dr. Spergel added, "If the universe were finite, then this
would rule out inflation and require something new."
The Search for Patterns
One Convincing Sign
So far, sporadic searches for repeating patterns of quasars
or distant galaxy clusters that would occur in a hall of
mirrors universe have been unsuccessful.
For finite universe aficionados, the first encouragement of
note was COBE's discovery that the universe appeared to be
deficient in large-scale fluctuations. There were no
structures extending more than about 60 degrees across the
sky. But the finding was subject to large statistical
uncertainties, astronomers said.
There are other possible explanations for the cutoff in
fluctuation size, Dr. Starkman explained. According to
inflation the biggest longest waves are created first, and
thus the missing notes are the earliest ones that would
have been strummed by inflation's guitar. Perhaps, he said,
this is telling us something about the beginning of
Dr. George Efstathiou of Cambridge University has pointed
out in a recent paper submitted to the Monthly Notices of
the Royal Astronomical Society that the Wilkinson satellite
data are also marginally consistent with yet another finite
shape, namely a sphere. In that case, fluctuations larger
than the radius of the sphere might be dampened, he said,
producing the observed cutoff.
The most convincing sign of a doughnut universe, if it
exists, astronomers say, could come from a search of the
satellite data now being performed by Dr. Spergel, Dr.
Starkman and Dr. Neil J. Cornish of Montana State
University. "We're looking for circles in the sky," Dr.
In a 1998 paper they point out that if the universe is
small enough, part of the cosmic background radiation,
which essentially fills the sky surrounding us, will hit
the sides of the "box" or the space war screen we are in
and appear on the other side. The result, in the simplest
case, would be identical circles on opposite sides of the
sky with the same patterns of hot and cold running around
In the simplest case, the size of the circles would depend
on the distance between the "walls" of the universe: the
smaller the universe, the bigger the circles.
Success or even a definitive failure is not guaranteed. "It
would be fantastic if something like that was found," Dr.
Hinshaw said of the circles.
But success or even a definitive failure is not guaranteed.
If the universe is finite but still much larger than
today's observable universe - 28 billion light-years in
diameter - the circles will not show. "Usually in science
when we see an intriguing pattern that appears to
contradict existing theory we do a better experiment," Dr.
Spergel wrote in an e-mail message, but in this case,
"Ultimately we will be limited by the fact that we can only
observe the `visible' universe."
Dr. Levin was doubtful, "I suspect every last one of us
would be flabbergasted if the universe was so small," she
said in an e-mail message. When she first heard about the
new satellite data, she reported, "I tried on the idea that
we were really and truly seeing the finite extent of space
and I was filled with dread.
"But I'm enjoying it too."