A Big Crunch is a hypothetical scenario in which the expansion of the universe eventually halts and reverses, leading to the collapse of the universe into a singularity.
The equations used to describe a Big Crunch are the Friedmann equations, which are a set of equations from general relativity that describe the evolution of the universe. These equations take into account factors such as the density and pressure of matter and energy in the universe.
Dark energy is believed to be the force behind the accelerating expansion of the universe. In a Big Crunch scenario, the effect of dark energy would decrease as the universe collapses, eventually becoming negligible.
A Big Crunch results in the universe collapsing into a singularity, while a Big Bounce is a theory that suggests the universe will collapse and then bounce back into a new cycle of expansion. The main difference between the two is whether or not the collapse results in a singularity.
Currently, there is no experimental evidence for a Big Crunch. Observations of the expansion of the universe suggest that the expansion is accelerating, making a Big Crunch less likely. However, further research and observations are needed to fully understand the fate of the universe.