Shaping a Universe 
Barry Cipra 

What links the cosmic microwave background (CMB) to the grand structure of the universe is the fabric of space-time. But just what is that fabric, and what can CMB measurements tell us about it?

In Einstein's general theory of relativity, space and time are knit together in a stretchy "manifold"--a mathematical object, every small patch of which looks roughly like a four-dimensional rubber sheet. Light rays follow contours of the manifold, called geodesics. On a flat plane, parallel rays from a distant object will stay the same distance apart as they approach an observer. But on a surface with "positive" curvature, like a sphere, approaching rays will move farther apart, making distant objects look bigger than normal. And on a surface with "negative" curvature, like a saddle, parallel beams will get closer together, making the object look smaller (see figures A).

[Figure 1] 


Because curved manifolds distort light differently from flat ones, they should also give rise to different sorts of CMB. The 1-degree-wide ripples that BOOMERANG observed were precisely what theory predicted for a flat universe--a conclusion that most physicists fully expect the Microwave Anisotropy Probe's (MAP's) maps to bear out.

Some researchers hope that MAP will give more specific information about the size and shape of the universe. "When we look at the microwave background, we're basically looking out to the surface of a sphere," explains David Spergel, an astrophysicist at Princeton University and a member of MAP's science team. If the universe is infinite, that "surface of last scattering" will give few clues about its shape. But if the universe is finite, then space-time--and the scattering surface nestled within it--must bend back on itself. A large enough sphere would then intersect itself in at least one circle, just as a disk wrapped around a dowel overlaps itself at the ends (see figures B).

[Figure 2] 


In fact, Spergel says, because light can take more than one path through curved space-time, astronomers would see each intersection not once but twice--as paired circles tracing out identical patterns of hot and cold spots in different parts of the sky. Spergel's group in the United States and a group headed by Jean-Pierre Luminet at the Paris Observatory are developing algorithms to look for such signatures in MAP's data.

Meanwhile, mathematician Jeff Weeks, a freelance geometer based in Canton, New York, has written a computer algorithm that turns paired circles into model universes. Easiest to visualize, Weeks says, is a "toroidal" universe slightly smaller than the surface of last scattering. In a 2D universe wrapped around a torus, he points out, astronomers would seem to see identical points on opposite walls of an imaginary box of space (see figures C). Similarly, astronomers in a 3D toroidal universe would see three pairs of circles in opposite directions.

[Figure 3] 


Toroidality is just the simplest of 10 different topologies for a "flat" finite universe. If the universe turns out to be curved--which is currently thought not to be the case--then there will be infinitely many more possibilities for Weeks's algorithm to sort through. "We'll start taking a look as soon as any sort of data is available," Weeks says. If the cosmos cooperates, they may not have long to wait, Spergel says: "In 2 years, we could know that we live in a finite universe."

   Volume 292, Number 5525, Issue of 22 Jun 2001, p. 2237.
   Copyright © 2001 by The American Association for the Advancement of Science.