In the inflationary model, a 1981 modification of the standard Big Bang thesis in which a brief but dramatic expansion occurred in the beginning, the universe has to have precisely the critical density. Since the inflationary Big Bang is widely supported by scientists because it so neatly explains much else about cosmic history, cosmologists want to believe its predictions of critical density. Otherwise they would have lost even more than their struggle to understand dark matter.
But so far, all measurements of cosmic mass fall well short of critical density, presumably indicating an open universe on its way to the big chill. At best, said Dr. Jeremiah P. Ostriker, a Princeton University astrophysicist, combinations of visible and likely dark matter add up to no more than 20 percent or possibly 30 percent of critical density.
"A lot of people don't think omega equals one," said Dr. Craig J. Hogan, a University of Washington astrophysicist. "They are the empiricists, the observers. They have discovered that there really isn't any evidence for high omega."
Dr. John N. Bahcall, an astrophysicist at the Institute for Advanced Study in Princeton, N.J., whose research on red dwarfs seemed to limit dark-matter possibilities, put it more bluntly. "I have a feeling that we just need to admit to ourselves that the emperor has no clothes," Dr. Bahcall said of the lack of observational evidence for critical density.
But like many specialists in the dark-matter hunt, Dr. Joel Primack, a theoretical physicist at the University of California at Santa Cruz, is not throwing in the towel. He and colleagues are developing new recipes combining neutrinos and cold dark matter like WIMP's that they say overcome previous objections to such hybrid solutions. Recent Japanese experiments, Dr. Primack noted, provided "wonderful clues" suggesting that neutrinos could well have detectable mass and so could account for some of the missing mass required to add up to critical density.
In simulations by supercomputers, the models with neutrinos alone or cold dark matter alone failed to lead to the construction of a universe looking like it does today. Neutrinos are "hot," in that they zip about rapidly, and could not have coalesced soon enough to have helped form galaxies. Cold dark matter, moving slowly and clumping easily, would have produced too much galactic clustering.
Even mixing the two, usually with about one-third neutrinos and two-thirds cold dark matter, has not passed computer-simulation tests; the hybrids still produce galaxies later in cosmic history than recent observations suggest. Some such mixed dark matter could finally pass the test, but many scientists are uncomfortable with such recipes, which smack of being cooked just for the purpose of crawling out of an observational and theoretical hole.
One of the most encouraging developments, astronomers say, is the growing conviction that neutrinos do have a finite mass. But will the mass be sufficient to account for a major fraction of dark matter?
Astronomers have not given up on finding more ordinary matter that could be part of the dark matter. They continue to search for low-mass stars, Jupiter-size planets and other faint objects, which they think may be littering the outer edges of galaxies. They are taking a closer look at the possibility that lower-mass black holes could play a more significant role in cosmic mass than had been thought.
"If nothing works and omega is not very close to one," Dr. Hogan said, "then we've got to find some way out."