In 1996 the French astronomer Dr. Jean-Pierre Luminet of the Paris Observatory and his colleagues Dr. Roland Lehoucq and Dr. Marc Lachieze-Rey, both of the Center for Astrophysical Studies in Saclay, France, developed a method called ''cosmic crystallography,'' using galaxy statistics to detect and diagnose the repeating periodic patterns that would be created in the sky by light going around and around in differently shaped universe.

Finite or Infinite?

Problems Are Posed For Favored Theory

Why would the universe want to do this to us? Partly to avoid the difficulties of the infinite, said Dr. Glenn Starkman, an astronomer at the Case Western Reserve University in Cleveland. Besides being difficult to create, an infinite universe is philosophically unattractive. In an infinite volume, he pointed out, anything that can happen will happen.

''Somewhere there are two guys having this same conversation,'' Dr. Starkman said in a telephone interview, ''except that one of them has a purple phone.''

Moreover, the idea that dimensions could be curled in loops occurs naturally in theories that try to unite gravity and particle physics, several physicists pointed out. For example, according to string theory, the leading candidate for a theory of everything, the universe actually has 10 dimensions -- 9 of space and 1 of time -- rather than the 4 we are familiar with. The extra dimensions are curled up into submicroscopic loops, like the threads in an uncut carpet pile, so that we don't notice them in ordinary life.

''This is the same idea on a very large scale,'' Dr. Smoot said.

Knowing that all nine of the spatial dimensions predicted by string theory are finite and thus on the same footing could help string theorists decide among the nearly endless possibilities allowed by the theory, scientists say.

But a finite universe would create big problems for the reigning theory of the Big Bang, inflation theory. It posits that the universe underwent a burst of hyperexpansion in its earliest moments. Among other things, it implies that the observable universe today, a bubble 28 billion light-years in diameter, is only a speck on the surface of a vastly greater realm trillions upon trillions of light-years across.

''There's no natural way yet proposed to get the inflation to stop and give a space that's big enough to house all the galaxies but small enough to see within the observable horizon,'' said Dr. Janna Levin, a Cambridge University cosmologist who wrote about finite universes in her 1992 book, ''How the Universe Got Its Spots, Diary of a Finite Time in a Finite Space.''