CLEVELAND — Astronomers said on Friday that they had determined the time in cosmic history when a mysterious force, 'dark energy," began to wrench the universe apart.

Some 5 billion years ago, said Dr. Adam Riess, an astronomer at the Space Telescope Science Institute in Baltimore, the universe experienced a "cosmic jerk." Before then, he said, the combined gravity of the galaxies and everything else in the cosmos was resisting the cosmic expansion, slowing it down. Ever since the jerk, though, the universe has been speeding up.

The results were based on observations by a multinational team of astronomers who used the Hubble Space Telescope to search out exploding stars known as Type 1a supernovae, reaching back in time three-quarters of the way to the big bang in which the universe was born.

The results should help quell any remaining doubts that the expansion of the universe is really accelerating, a strange-sounding notion that has become one of the pillars of a new and widely accepted model of the universe. The theory maintains that the universe is full of mysterious dark matter and even more mysterious dark energy.

"This gives great confidence that we've been on the right track," said Riess, who announced his results at a meeting on the future of cosmology, sponsored by the Center for Education and Research in Cosmology and Astrophysics at Case Western Reserve University and by the Kavli Institute.

Dr. Joseph Lykken, a physicist at the Fermi National Accelerator Laboratory, known as Fermilab, said, "I could go home now and be happy."

Knowing how and when the jerk took place, astronomers said, is an important step in the process of figuring out just what the dark energy is.

"He gave us information about when the universe hit the gas pedal," said Dr. Michael Turner, a cosmologist at the University of Chicago who is director of mathematics and physics at the National Science Foundation. Different theories of dark energy, he explained, predict different times for the transition.

The result was also a kind of personal vindication for Riess, who was a pivotal member of one of two competing groups of astronomers, one led by Dr. Brian Schmidt of the Mount Stromlo and Siding Spring Observatories in Australia, the other by Dr. Saul Perlmutter of the University of California's Lawrence Berkeley Laboratory, who discovered the cosmic acceleration five years ago. The groups were using supernovae to chart the expansion of the universe at different times in the past.

The goal was to measure how much the universe was being slowed by the collective gravity of the cosmos and determine whether it would go on forever or recollapse in a "big crunch" one distant day.