If the cosmological constant were zero, the expansion of the universe would not necessarily stop. The cosmological constant, often denoted by the symbol Λ (lambda), is a term in Einstein's field equations of general relativity that represents a form of energy associated with empty space or vacuum. It acts as a repulsive force on cosmic scales and is responsible for the observed acceleration of the universe's expansion.
When the cosmological constant is positive, as suggested by observational evidence, it counteracts the attractive gravitational force between matter and causes the expansion of the universe to accelerate. If the cosmological constant were zero, the expansion of the universe would not experience this additional acceleration, but it would not necessarily come to a halt.
The fate of the universe's expansion depends on the overall energy density of the universe, which includes contributions from matter (including both ordinary matter and dark matter) and radiation. The critical parameter that determines the ultimate fate is the ratio of the total energy density to the critical density.
If the total energy density is greater than the critical density, the universe will continue to expand forever, although the rate of expansion may slow down over time. This is known as an open or "unbound" universe.
If the total energy density is equal to the critical density, the universe will also continue to expand forever, but the rate of expansion will gradually approach zero. This is known as a flat universe.
If the total energy density is less than the critical density, the universe will eventually stop expanding and start contracting under the influence of gravity. This is known as a closed or "bound" universe.
The cosmological constant affects the expansion rate but is not the sole determinant of the universe's fate. Other factors, such as the energy content and curvature of the universe, also play significant roles.