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The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potentially followed by a reformation of the universe starting with another Big Bang. The vast majority of evidence indicates that this theory is not correct. Instead, astronomical observations show that the expansion of the universe is accelerating, rather than being slowed down by gravity, suggesting that it's more likely for a Big Freeze to occur.
The Big Crunch scenario hypothesized that the density of matter throughout the universe is sufficiently high that gravitational attraction will overcome the expansion which began with the Big Bang. The FLRW cosmology can predict whether the expansion will eventually stop based on the average energy density, Hubble parameter, and cosmological constant. If the metric expansion stopped, then contraction will inevitably follow, accelerating as time passes and finishing the universe in a kind of gravitational collapse.
A more specific theory called "Big Bounce" proposes that the universe could collapse to the state where it began and then initiate another Big Bang, so in this way the universe would last forever, but would pass through phases of expansion (Big Bang) and contraction (Big Crunch).
Experimental evidence in the late 1990s and early 2000s (namely the observation of distant supernovae as standard candles, and the well-resolved mapping of the cosmic microwave background) led to the conclusion that the expansion of the universe is not being slowed down by gravity but is instead accelerating. The 2011 Nobel Prize in Physics was awarded to researchers who contributed to making this discovery.