Obtaining evidence of a finite topology by looking for similarities between images of galaxies or quasars that appear in different directions, representing different times in their past, has proved extremely difficult. For one thing, quasars and galaxies evolve too quickly for astronomers to easily match up images of the same object in different epochs.

A clear signature may be written in the microwave sky, however. "What has invigorated the field is the realization that microwave background observations would be a clean probe of topology," Spergel says.

At its earliest moments, the universe is thought to have been a nearly uniform, scrunched plasma of photons and various particles, such as protons, electrons, and neutrinos. About 300,000 years after the Big Bang, that opaque plasma cooled enough to allow neutral atoms to form. Instead of being constantly scattered by particles, photons were then free to cruise the universe essentially unimpeded.

As viewed from Earth, which is immersed in this cosmological radiation, the photons appear to come from a sphere centered on the observer. Called the surface of last scattering, that sphere has a radius equal to the speed of light multiplied by the travel time since those photons’ last interaction with matter. Because of the subsequent expansion of the universe, the photons have shifted to lower wavelengths, and they are now observable as the cosmic microwave background.

If the universe has a finite size, this expanding sphere “can wrap all the way around and intersect itself,” Weeks says.

The intersection of one sphere with itself is seen as a circle. In a finite, multiply connected universe, an observer at the center of such a sphere would see the same circle of points in two different directions.

Spergel, Neil J. Cornish of the University of Cambridge in England, and Glenn D. Starkman of Case Western have proposed a scheme for detecting such circles in the sky.

A map of the cosmic microwave background shows tiny temperature fluctuations. The idea is to identify pairs of circles by matching point by point the pattern of temperature fluctuations along each circle. “That’s what would tell you you’re looking at the same circle of points in two different directions,” Weeks says.

Moreover, “it’s highly unlikely that the universe would be just the right size that you would get just one pair of intersections—that it’s small enough that you can see around in only one direction,” he adds. “There should be thousands of pairs of matched circles.”

Once those circles have been identified, researchers can determine the specific type of three-dimensional manifold that fits the observations. “The pattern of circles is like a signature for the space,” Weeks says. In the hyperbolic case, “we would probably get a small number of very large circles and a tremendously large number of small circles.”
“If we find circles, we would actually be able to build a model of the universe,” Starkman notes.

Microwave data from the Cosmic Background Explorer spacecraft (SN: 1/10/98, p. 20; 5/2/92, p. 292) had insufficient resolution to permit a fruitful search for circles. However, the launch in a few years of the sun-orbiting Microwave Anisotropy Probe (MAP) spacecraft and later of the European Space Agency’s Planck satellite promise measurements of sufficiently high resolution to make a quest for circles feasible (SN: 6/7/97, p. 354).

“We don’t know whether topology is important in cosmology, but it could be,” Spergel says. “We’ll be able to find that out reasonably soon, and if it is, it would be very exciting.”

The general theory of relativity posits that gravity is essentially a geometric effect—in other words, the theory links mass with the local curvature of space. Interestingly, it says nothing about the shape of the universe—the overall form of the three-dimensional spatial component of relativity’s four-dimensional space-time.
Finding out this topology “would have a great impact on our vision of the universe,” says Janna J. Levin of the Center for Particle Astrophysics at the University of California, Berkeley.

“It would tell us about physics beyond general relativity,” Spergel adds.

Knowing the topology, researchers could independently determine the ratio of the universe’s density to its critical value and reconstruct the state of the universe that gave rise to the cosmic microwave background. They could also gain insights into quantum gravity, quantum chaos, string theory, and other ideas at the forefront of efforts to construct a unified theory of force and matter.

“Cosmologists are used to thinking of looking out at the universe and measuring the prehistory of other regions of the universe,” Cornish, Spergel, and Starkman conclude in the Jan. 6 Proceedings of the National Academy of Sciences. “If we are fortunate enough to live in a compact hyperbolic universe, we can look out and see our own beginnings.”

“The mathematics of models for finite universes is rich,” Spergel notes. “We’ve only just begun to explore the physics of those possibilities.”

References:

Cornish, N.J., D.N. Spergel, and G.D. Starkman. 1998. Measuring the topology of the universe. Proceedings of the National Academy of Sciences 95(Jan. 6):82.

Levin, J., E. Scannapieco, and J. Silk. Preprint. Is the universe infinite or is it just really big?

Levin, J.J., et al. Preprint. Flat spots: Topological signatures of an open universe in COBE sky maps. 

Tag: See around the universe?