Where is the rest of the universe?

One of the fundamental - and awkward - challenges astronomers face is the simple fact that there's more to the universe than meets the eye. It's awkward because nobody knows just how much mass the cosmos contains or of what much of that mass consists.

It's challenging because astronomers need a good estimate of the cosmic mass to know what kind of universe we inhabit. Also, in trying to decide what that mass might be, scientists find even the basic laws of physics to be an uncertain guide.

That is why a new estimate of the mass, made by Victor E. Viola of Indiana University, is likely to draw considerable scientific interest. He was scheduled to present it today at the International Chemical Congress of Pacific Basin Societies in Honolulu.

In defining their idea of the cosmos, modern cosmologists think in terms of three possible types of universe.

* An open universe - one that does not have enough mass for gravity to halt its expansion. It expands forever at a constant or at an accelerating rate. Eventually its stars burn out, and the universe, in effect, dies.

* A closed universe - one with enough mass to halt and eventually reverse its expansion. It ends as an infinitesimal, superdense mass similar to the ''cosmic egg'' from which it is believed to have been born in the so-called big-bang primordial explosion. Whether or not it would then bounce back in yet another ''big bang'' is an unanswered question.

* The in-between case, where there is only enough mass to gradually slow, but not quite stop, the universe's expansion. Again, the stars would eventually burn out and the universe die.

Viola says he now is virtually certain that we live in an open universe, one that will expand forever.

He draws this conclusion from studies of the element lithium, whose abundance is believed to reflect conditions of the big bang itself. Specifically, he's interested in the relative abundance of two forms of lithium - Li-6 and Li-7. These forms, called isotopes, are chemically identical but have slightly different masses.

There is twice as much Li-7 as Li-6 in new lithium, which is formed today by the action of cosmic rays. However, in lithium generally, the heavier isotope is 12 times more common than the lighter form. This excess of heavy lithium is believed to be due to the big bang, which made lithium by a different process than that which forms the element today.

Calculating back from present lithium data, Viola has estimated the total mass of energy and matter in the early universe. He notes that this should be roughly the same as the cosmic mass today. That total is only one-tenth of the mass needed to make the universe contract.

''The answer is unequivocal, . . .'' Viola says. ''The universe is open.''

While this is not the first such lithium-based estimate, Viola says it is based on the most comprehensive data yet employed. He notes that the best previous mass estimates used the cosmic abundance of deuterium (doubly heavy hydrogen). This too was set by the ''big bang.'' And it, too, indicated an open universe. Now, Viola says, this conclusion has been confirmed by his independent assessment based on lithium data.

However, while this suggests an upper limit for the mass of the cosmos, it does not clear up the puzzle of the ''missing'' mass. By studying the motions of stars within galaxies, galaxies within clusters of galaxies, and clusters within larger gravitationally bound systems, astronomers can estimate the total mass within those systems. The gravitational influence of that mass governs the motions. When this process is carried out for the entire universe, astronomers find that the cosmos must contain 10 to 100 times as much mass as that of the stars and other luminous material.

They conclude that it is likely to be some kind of undetected cold, dark matter. But what it is and where it is located is one of the biggest questions in astronomy today. The puzzle is compounded by the realization that there may not be enough material made of ordinary particles, such as protons and neutrons, to close the mass gap. Such material would include rocks, dead stars, planets, dust, gas, and other ordinary material not yet detected. If there is not likely to be enough of such material, theorists are forced to think about more exotic forms of matter - forms which have not yet even been shown to exist.

These forms include gravitrons (particles associated with gravitational fields), magnetic monopoles (magnetic particles with only a single north or south pole), and massive neutrinos. Speculative theories that deal with basic physical forces as different aspects of a single unified force predict that such particles could form in the early moments of the ''big bang.'' But only neutrinos have ever been detected, and these have been considered to be particles which carry energy but which have no intrinsic mass at all.

If neutrinos did have mass - even as tiny a mass as one ten-thousandth the mass of an electron - they are believed to be so numerous that they could account for the ''missing'' material.

Some experiments have suggested just such mass for neutrinos. But the results have not generally been convincing. Last month, at a seminar at the University of Sussex, British physicist Carlos Frenck presented calculations which he said would ''knock the last nails in the coffin of the massive neutrino theory.'' He explained that, if neutrinos had the proposed mass, they would have disappeared during the expansion of the universe to a much greater degree than is actually observed.

In yet another attempt to settle the question experimentally, a team of scientists from the University of California at Santa Barbara and the Lawrence Berkeley National Laboratory, run by the University of California at Berkeley for the US Department of Energy, are studying the radioactive decay of germanium. The experiment, which began last month, is looking for events that occur about once in a trillion trillion years. Since the germanium sample has several trillion trillion atoms, the experimenters hope to see five or six candidate events a year. The equipment is located 600 feet below Oroville Dam in northern California to screen out interference from cosmic rays.

Ordinarily, an unstable germanium nucleus decays by emitting an electron and a neutrino. But in rare cases, physicists theorize it might emit two electrons and no neutrinos. These are the postulated rare events - events that have never been observed - for which the scientists are looking. If found, this effect would indicate that the neutrino has a small amount of intrinsic mass.

Until such experimental evidence is in hand, astronomers are left with no proof at all that such exotic forms of matter even exist, let alone that they could account for the ''missing'' mass of the universe.

Thus, in confronting the basic questions of what are the nature, history, and future of the cosmos, astronomers can only resort to speculation. As Cornell University astrophysicists Stephen E. Schneider and Yervant Terzian note in reviewing the subject in the current issue of American Scientist, this state of ignorance ''is fueling a heated debate over many of our most basic assumptions about the nature of the universe.''