The key to this hypothesis is the amount of dark energy in the universe. If the universe contains enough dark energy, it could end with all matter being pulled apart.
The key value is w, the ratio between the dark energy pressure and its energy density. At w < -1, the universe will eventually be pulled apart. First the galaxies would be separated from each other, then gravity would be too weak to hold individual galaxies together. Approximately three months before the end, solar systems will be gravitationally unbound. In the last minutes, stars and planets will come apart, and atoms will be destroyed a fraction of a second before the end of time.
The authors of this hypothesis calculate that the end of time would be approximately 3.5×1010 years after the Big Bang, or 2.0×1010 years from now.
See also: List of astronomical topics, Big Crunch, Accelerating universe, Ultimate fate of the Universe
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