February 16, 1998
Ari Buchalter, a graduate astronomy student, and David Helfand, professor of astronomy at Columbia, 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 Mr. 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 Germany 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 homogeneous 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," Mr. 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.
Mr. 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, Professor Helfand has participated in a survey to map sources of radio waves -- stars, quasars or galaxies -- 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. The project has already discovered hundreds of thousands of radio sources never before seen and is expected to find more than a million when the work is finished.
The problem with previous studies that supported Euclid's view of the universe, or that produced ambiguous results, Mr. Buchalter said, may be that astronomers did not carefully define the set of objects that would allow the ruler effect to be confirmed or disproved. Previous studies had compared galaxies by fixed angular size -- the amount of space they occupied in a telescope's view, not in real space. Mr. Buchalter deduced a way to compare objects in the same range of physical sizes, only one of several definitional problems he was able to resolve.
Professor Helfand's collaborators on FIRST, and co-authors with him and Mr. Buchalter of the paper in The Astrophysical Journal, are Robert H. Becker, professor of physics at the University of California at Davis, and Richard L. White, associate astronomer at the Space Telescope Science Institute in Baltimore.
The research was supported by the National Science Foundation, the Space Telescope Science Institute, the National Geographic Society, Columbia University and Sun Microsystems.
Carnegie Mellon University 13 February 1998
"Our work does favor a high value for Omega. This has interesting consequences for cosmology, meaning the universe may eventually stop expanding and may even re-collapse. However, people shouldn't be worried, it will take an infinitely long time to happen," cosmologist Robert Nichol said. His work puts scientists one step closer to answering the question of how the universe will end.
Using new samples of X-ray emitting clusters of galaxies, Nichol and Daniel Reichart, a Ph.D. candidate at the University of Chicago, said they have been able to obtain a measurement that leads them to believe the value of Omega may be one. Omega, one of the two main parameters that explain the evolution of the whole universe -- the other is Hubble's Constant -- is the ratio of the observed average density of the universe compared to a critical value. This critical value is equivalent to only 11 hydrogen atoms per cubic centimeter and is the density of mass needed to reverse the expansion of the universe, by gravity, and make the universe turn around and retract, ending in the so-called "Big Crunch." Therefore, if the value of Omega is measured to be exactly one, the universe will eventually stop expanding. If Omega is below one, then the universe will expand forever with no end.
The data used by Nichol and his collaborators was obtained from the ROSAT, the ROentgen SATellite, and Einstein X-ray Observatories developed through cooperative programs between NASA, Germany and the United Kingdom. The data set was developed for analysis by an international group of astrophysicists including Kathy Romer of Carnegie Mellon, Mel Ulmer of Northwestern University, Francisco Castander and Brad Holden at the University of Chicago, and Chris Collins and Doug Burke of Liverpool John Moores University.
A measurement of Omega is central to all theories of cosmology, especially a theory called inflation that was introduced in the 1980s to explain, in part, why many cosmologists thought the value of Omega should be one. Nichol said that if Omega is observed not to be one, then many theorists will be looking for more exotic theories for the origin of the universe.
In the hot Big Bang Theory, the observable universe began from a rapidly expanding point, roughly fifteen billion years ago. Since then, the universe has continued to expand, gradually increasing the space (and time) between our Galaxy and external galaxies. This expansion of the universe "stretches" the wavelength of that light that is traveling to us from these distant galaxies, thus making their light appear redder. This measured "stretching" is called redshift and is an important measure of distances in the universe because of Hubble's famous law.
Nichol said this new data probes some of the "highest redshifts offered by present cluster surveys." By comparing the number density of clusters seen at these great distances to that seen in the near universe, Nichol explained that one can immediately obtain an insight into the value of Omega.
"The signal is very strong. For example, our standard cosmological theories tell us that if Omega is exactly equal to one, then the number of massive clusters in the universe at half it's present age should be 100 times fewer than that predicted for a universe with a low Omega. This is a big signal to measure and can easily differentiate between low and high values of Omega. That is basically what we have done with this new data set," he said.
In addition to stopping the expansion of the universe, a high value for Omega implies the existence of 'dark matter' made from exotic elementary particles. Nichol explained, "Omega measures the gravitational influence of all the mass in the universe, however, we can only see a fraction of this mass with our telescopes. About 90 percent of the mass could be invisible to our traditional observatories; we only see the tip of the iceberg."
During the next decade, the pursuit of Omega will heat up, culminating with the launch of two microwave satellites -- NASA's Microwave Anisotropy Probe (MAP) and the European Space Agency's Planck. These satellites will study the Cosmic Microwave Background in exquisite detail and should be able to measure Omega to about 99 percent accuracy.
"Cosmologists are in pursuit of one of the remaining Holy Grails of physics; the exact value of Omega," said Nichol. "Now, with many new measurements on the horizon, I believe we are at the beginning of the end of our pursuit of Omega."
The race for the answer is also on from ground-based efforts like the search for distant supernovae and Carnegie Mellon's millimeter telescope, Viper, which is beginning its operations at the Pomerantz Observatory at the South Pole. Nichol is planning to extend his work using NASA's Advanced X-ray Astrophysics Facility (AXAF) satellite due to be launched later this year.