MAP LAUNCH:
Shaping a Universe Barry Cipra 
What links the cosmic microwave background (CMB) to the grand structure of the universe is the fabric of spacetime. 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 fourdimensional 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] ILLUSTRATION: A. STONEBRAKER
Because curved manifolds distort light differently from flat ones, they should also give rise to different sorts of CMB. The 1degreewide ripples that BOOMERANG observed were precisely what theory predicted for a flat universea 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 spacetimeand the scattering surface nestled within itmust
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] ILLUSTRATION: A. STONEBRAKER
In fact, Spergel says, because light can take more than one path through curved spacetime, astronomers would see each intersection not once but twiceas 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 JeanPierre 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] ILLUSTRATION: A. STONEBRAKER
Toroidality is just the simplest of 10 different topologies for a "flat" finite universe. If the universe turns out to be curvedwhich is currently thought not to be the casethen 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.
