A REPORT ON THE SHAPE OF
Analysis of recent data collected about the cosmic background radiation has yielded some surprising insights into the shape and size of the universe. As reported in issue 114, the background radiation has an equator, and that equator is the same as the ecliptic, the path the sun traces out through the zodiac in the course of a year. In this paper, however, we focus on the latest findings suggesting that the universe may be a torus (doughnut, or donut, as we backwoods “Americans” spell it), or a dodecahedron, or maybe a sphere after all.
Imagine a donut, a toroid. Now imagine that is the picture of space. Rather than being infinite in all directions, albeit bounded, as the common theory maintains, the universe could be radically smaller in one direction than the others, even as a donut has a thinner diameter for the circular cross-section of the toroid than for its outer diameter.
According to Dr. Max Tegmark of the University of Pennsylvania, “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.” He said that on the basis of temperature measurements of the dark night sky, the radiation variously known as the Cosmic Microwave Background (CMB) radiation, also known as the 3-degree black body radiation.
In July of 2003, Tegmark, his wife Angélica de Oliveira-Costa, and Andrew J. S. Hamilton reported on the radiation what was left after subtracting out the contribution due to the Milky Way. They end their abstract with: “We argue that our CMB map is clean enough that the lowest multipoles [the lowest multipole is a dipole, where radiation is concentrated in two opposite areas of the sky, a quadrupole has the radiation concentrated in four areas of the sky like at the corners of a square, etc.—Ed.] can be measured without any galaxy cut [meaning leaving the galaxy-covered area blank—Ed.], and obtain a quadrupole value that is slightly less low than that from the cut-sky WMAP [Wilson Microwave Anisotropy Probe —Ed.] team analysis. This can be understood from a map of the CMB quadrupole, which shows much of its power falling within the Galaxy cut region, seemingly coincidentally. Intriguingly, both the quadrupole and the octopole [8 poles, positioned at the eight corners of a cube—Ed.] are seen to have power suppressed along a particular spatial axis [direction—Ed.], which lines up between the two, roughly towards Galactic coordinates (l, b) ~ (-110°, 60°) in Virgo.”
More descriptively, this position lies in the plane of the Local Supercluster of galaxies. The Supercluster is like a galaxy made up of galaxy clusters instead of stars. It streams around the sky like a faint version of the Milky Way, passing from Virgo, Coma Berenices (with a spur into Leo), on through Canes Venatici, Ursa Major, and on to Camelopardalis where it thins out and fades behind the Milky Way. It emerges in Andromeda and continues through Pisces, Cetus, Sculptor, Grus, Indus, and Pavo. In eastern Ara it is obscured again by the Milky Way, emerging at Lupus, and from thence through Centaurus, Hydra, and back to Virgo. Several spurs branch off from the Supercluster, which is not mentioned much anymore in the astronomical literature.
If true, the donut universe would force cosmologists to reconsider once again their theories about what happened in the earliest moments of the Big Bang. After all, the cosmic background radiation is believed by most astronomers to be the afterglow of the Big Bang itself, a portrait of the universe when it was allegedly 380,000 years old. Since galaxies do not form in the original Big Bang model, it was postulated that the early Big Bang did not expand smoothly but became lumpy, and that the lumps became galaxies, and clusters of galaxies, and platters or walls of clusters of galaxies, and so forth. The latest view is to model these irregularities as microscopic fluctuations born during the first instant of time and then amplified into sound waves as the universe expands and matter and energy slosh around.
By analyzing these waves, cosmologists can fine-tune their modifications until they can “predict” many of the postulated characteristics of the universe such as its age and density. Although there has been much fanfare in the press that these observations validate the Big Bang, the celebration is premature. The observations yield yet another unexpected problem.
According to relativity, the Big Bang should produce a universe that is “infinite, yet bounded.” Such a results allows the earth to look like it is at a special place or center of the universe without it having to be so. The relativistic model of the Big Bang allows each and every spot in the universe to look as if it is in the center and at rest. In such a universe, the slosh-waves in the cosmic fireball should appear randomly distributed 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. Thus cosmologist James Peebles, of Princeton, continues to be vindicated when he said, “Cosmologists have built a house of cards and it stands.”
The refined map by Tegmark et al., referred to earlier, shows that the universe appears lumpier in one direction in space than it does in another. When the finer variations were taken out of the map, the remaining large-scale variations formed a line across the sky. If the universe is finite in one dimension, like a cylinder or a doughnut, 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 down to a particular note such as an E, determined by its length and diameter. 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 plane. Nobody is yet claiming that this is a revolution I cosmology. The notion of a special direction is not on as firm a ground as the discovery of a size limit on large structures.
Dr. Alexei Starobinski, a theorist at the Landau Institute in Moscow, and Dr. Yakov B. Zeldovich, proposed in 1984 that the universe could have been formed as a donut. 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 response to being questioned about the donut universe results.
A Hall Of Mirrors?
The new work involves topology, the branch of mathematics which deals with shapes. To a topologist, a donut is the same shape as a human, with the digestive tract as the “donut hole.” This is because each object has one hole, the two can be deformed into each other and are thus topologically equivalent. The simplest topology is the infinite space of the Euclidean geometry, but cosmologists have a hard time conceiving how an infinite universe could have appeared in that kind of flat space. To them, it seems more reasonable that God created a finite universe which looks infinite. These models are called “compact universes.”
The simplest compact universe is one called a 3-torus, a donut wrapped in three dimensions. This object is essentially impossible to visualize: it is like a cube whose opposite sides are somehow glued together. In a way, it is like one of the old video games where an object disappearing on the right hand side of the screen simultaneously reappears on the left hand side. Such a universe would be like being inside a hall of mirrors. 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 the cube and back in the other.
Such a reflecting universe is not limited to cubes and doughnuts. Universes composed of various polyhedrons glued together in various ways will also loop light around from one face to its opposite face.
Big and Little Loops
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 will happen.
Moreover, the idea that dimensions could be curled in loops occurs naturally in theories that try to unite gravity and particle physics. For example, according to string theory, the leading candidate for a theory of everything, the universe actually has ten dimensions, nine of space and one of time, instead of the four we normally think of. The extra dimensions are curled up into submicroscopic loops, so tiny that we don’t notice them in ordinary life. The torus universe mentioned above is the same idea, but on a very large scale.
As we mentioned earlier, a finite universe creates 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. It seems that Tegmark’s observations rule out inflation.” But I remind the reader that the first inflationary model, reported circa 1972 and promptly ignored, yielded the present universe in roughly 100,000 years, far too little time for life to have evolved without God, and thus abhorrent to secular scientists of this age.
In a more recent paper, Jean-Pierre Luminet et al. reported the following in their abstract:
Cosmology’s standard model posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales.... Temperature correlations across the microwave sky match expectations on scales narrower than 60°, yet vanish on scales wider than 60°. Researchers are now seeking an explanation of the missing wide-angle correlations.... One natural approach questions the underlying geometry of space, namely its curvature ... and its topology. In an infinite flat space, waves from the big bang would fill the universe on all length scales. The observed lack of temperature correlations on scales beyond 60° means the broadest waves are missing, perhaps because space itself is not big enough to support them.
Here we present a simple geometrical model of a finite, positively curved space—the Poincaré dodecahedral space—which accounts for WMAP’s observations with no fine-tuning required. Circle searching [see below —Ed.] may confirm the model’s topological predictions, while upcoming Planck Surveyor data may confirm its predicted density of W0 @ 1.013 > 1. If confirmed, the model will answer the ancient question of whether space is finite or infinite, while retaining the standard Friedmann-Lemaître foundation for local physics.
Luminet helped pioneer the study of cosmic crystallography and his work has been reported before in Panorama. Here he claims superiority for his model, by virtue of a better fit, than the toroidal model.
But Maybe the Universe Is a Sphere after All
So far, searches for the repeating patterns of quasars or distant galaxy clusters that would occur in a compact universe have been unsuccessful. The first encouragement of note was the aforementioned 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 size. According to inflation, the longest waves appeared first, and thus the missing notes are the earliest ones that would have been emitted. Some think that the new evidence may, instead, say something about the beginning of inflation.
Dr. George Efstathiou of Cambridge University pointed out in a recent paper submitted to the Monthly Notices of the Royal Astronomical Society that the Wilkinson satellite data are still 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 Circular Quest for Observational Evidence
The most convincing sign of a donut universe, if it exists, could come from a search of the satellite data now being performed by the team of Spergel, Starkman, and Cornish of Montana State University. They are looking for circles in the sky.
In a 1998, they pointed out that if the universe were small enough, part of the cosmic background radiation would hit the sides of the “box” 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 them. The size of the circles depends on the distance between the walls of the universe: the smaller the universe, the bigger the circles. If the universe is finite but much larger than today’s observable universe (14 billion light-years in radius), the circles will not show.
The Infinite Universe and the Bible
What does the Bible have to say about an infinite universe? This was a hot topic of debate in the sixteenth and seventeenth centuries. The consensus was that the universe is finite. One reason given for that conclusion is that an infinite universe could never be finished, but God ended creation of the universe in a finite time, namely six days. 
Later arguments focused on physical evidence. For instance, in an infinite universe every line of sight must end at the surface of a star. Thus the entire sky, both day and night, should be as bright as the surface of the sun. This is called Olbers’ Paradox. Modern science has invoked the expanding universe as a solution to Olbers’ Paradox but that merely transforms the problem to another form. You see, an infinite universe must also be eternal. An infinite time must come to pass before this present and an infinite time will follow after. Since energy can neither be created nor destroyed, the energy density of the universe should reach the same as expressed in Olbers’ paradox.
Finally, if the universe is infinite, it has the same properties as God, including having no beginning. If that is so, would God still be God?
Of Atom Bombs and Thunder Storms
A single thunderstorm can release to the atmosphere energy equivalent to a megaton hydrogen bomb. And since some fifty thousand thunderstorms break forth on earth every day, the daily energy release equals a billion of tons of TNT.
—Walter Orr Roberts, 1972.
“We’re Doing Something About the Weather!”
National Geographic Magazine, 141(4):518, (quote, p. 528).
To an optimist, the glass is half full.
To a pessimist, the glass is half empty.
To an engineer, the glass is twice as big as it needs to be.
 Panorama, 2003. “Preferred directions in the universe?” B. A., 13(106):123-125.
 Tegmark, M., A. de Oliveira-Costa, & A. J. S. Hamilton, 2003. “A high resolution foreground cleaned CMB map from WMAP,” to appear in Physical Review D, [arXiv.org/pdf /astro-ph/0302496].
 Luminet, J.-P., J. Weeks, A. Riazuelo, R. Lehouck, & J.-P. Uzan, 2003. 9 October issue of Nature. “Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background,” a slightly different version of the Nature paper can be found at arXiv.org/pdf/astro-ph/0310253.
 Panorama, 2002. “A small spherical universe after all?” B. A., 12(99):38-40.
 Also see Byl, J., 2000. “God, Space and Time,” B. A., 10(94):10.
 Daneau, Lambert, 1575. The Wonderful Workmanship of the World,
 Bouw, G. D., 1991. “Olbers’ Paradox: Why Is the Night Sky Dark?” B. A., 1(56):11.