VOL. 23, NO. 15	FEBRUARY 20, 1998

Ari Buchalter and David Helfand use a concave mirror to demonstrate the idea that objects further away can look larger. Their hands are about five inches from the mirror’s surface. Record Photo by Eileen Barroso.

hat shape is the universe? It’s probably an expanding, multidimensional equivalent of either a sheet of paper, a sphere or a saddle, according to Columbia astronomers, who report in the Feb. 20 issue of The Astrophysical Journal that they can shed new light on a problem that has stumped scientists for decades.

  Ari Buchalter, a graduate astronomy student, and David Helfand, professor of astronomy, have devised a way to examine radio telescope measurements of distant galaxies to determine whether the universe is “open” and will expand forever, “closed” and will eventually collapse, or “flat” and will attain some kind of equilibrium. They have studied 103 galaxies so far, and believe they can draw valid conclusions if they obtain results from 500 such galaxies, a project that should take another year or so.

  “There’s lots of evidence pointing to an open universe,” said Buchalter, who is writing a doctoral dissertation at Columbia based on his research. “Theorists say the universe is flat. Observers say it’s open. If we can get 500 of these galaxies, we should be able to rule in favor of one of them.”

  Such a study would complement information being gathered by two satellites being launched to study this very question. The National Aeronautics and Space Administration has approved the Microwave Anisotropy Probe (MAP), to be flown in 2000 to carry out measurements of the cosmic microwave background radiation, which will give scientists information about the density of the universe and allow them to deduce its shape. The European Space Agency has approved a subsequent, more precise mission, the Planck Surveyor.

  Since the mid-20th century, astronomers have rejected the notion of a static, or Euclidean, universe, in which parallel lines extend infinitely without meeting. Instead, they now believe that space ultimately curves at great distances, and that parallel lines do touch each other, much as they would if drawn on the surface of a curved object. The only unresolved question has been the shape of that curve.

  Such a geometry is called Riemannian, after Georg Friedrich Riemann, a 19th-century German mathematician. Riemannian geometry is best understood as projected on a sphere, not a plane, as Euclid’s was. Riemann showed that any number of lines could be drawn through two points and that the sum of the angles of a triangle is always more than 180 degrees. Albert Einstein would later show that Riemann’s concept of reality was closer to the truth than Euclid’s was.

  Though astronomers believe the large-scale universe is homogenous and isotropic—that is, the same everywhere and appearing the same in all directions—they describe its possible shapes as multidimensional equivalents of two-dimensional objects. A flat universe is thought of as a flat piece of paper; a closed universe as a sphere and an open universe as a saddle or potato chip—a many-dimensioned hyperbola. Though astronomers can write equations for these shapes, they admit that no one can really grasp what the shape would look like.

  “We’re a bit like ants living on the surface of a balloon,” Buchalter said. “They know the surface they can perceive is two-dimensional, and they know it is expanding because they can observe the distance between points increasing. But they simply can’t grasp the existence of a third dimension—through the balloon. We’re three-dimensional creatures unable to grasp four-dimensional space. But in this higher-dimensional space, there is some shape to the universe.”

  Astronomers have tried to determine the shape of the universe by trying to discover how objects that are actually the same size, such as certain classes of galaxies, appear larger or smaller at greater distances. In static, Euclidean space, a foot-long ruler would look smaller and smaller the farther away it was placed. But according to the theory of relativity, in Riemannian space, a ruler moving away from the observer would appear to become smaller at first, then larger, as the very fabric of space-time curved back around to the observer.

  Buchalter’s initial findings are not promising for Euclid. Instead of sending a ruler out into space, he carefully defined a set of 103 double-lobed quasars, galaxies emitting jets of gas in two opposite directions, that are usually about the same size and can thus serve as a ruler. The data, obtained from a radio telescope survey, can be interpreted to support any of the three Riemannian universes—but not a Euclidean one.

  Since 1993, Helfand has participated in a survey to map sources of radio waves in a quarter of the sky visible from Earth. The project, dubbed FIRST, or Faint Images of the Radio Sky at Twenty-cm, uses the National Radio Astronomy Observatory’s Very Large Array, 27 dishes arranged in a seven-mile-long Y-shape 60 miles west of Socorro, N.M. Helfand’s collaborators on FIRST, and co-authors with him and Buchalter of the paper in The Astrophysical Journal, are Robert H. Becker, professor of physics at U.C.–Davis, and Richard L. White, associate astronomer at the Space Telescope Science Institute in Baltimore. It was supported by the NSF, the Space Telescope Science Institute, the National Geographic Society, Columbia and Sun Microsystems.