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If the density of the universe is less than the critical density which is proportional to the square of the Hubble constant, then the universe will expand forever, like the green or blue curves in the figure above. If the density of the universe is greater than the critical density, then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch", like the orange curve. However, recent observations of distant supernova have suggested that the expansion of the universe is actually accelerating or speeding up, like the red curve, which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as the "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever.
There is a growing consensus among cosmologists that the total density of matter is equal to the critical density, so that the universe is spatially flat. Approximately 3/10 of this is in the form of a low pressure matter, most of which is thought to be "non-baryonic" dark matter, while the remaining 7/10 is thought to be in the form of a negative pressure "dark energy", like the cosmological constant. If this is true, then the universe will continue in a runaway expansion, as depicted in the red curve above.
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